Hamdi Abdelhamid | The University of Tokyo (original) (raw)

Papers by Hamdi Abdelhamid

Research paper thumbnail of Solitary, explosive and periodic solutions for electron acoustic solitary waves with non-thermal hot ions

Advances in Space Research, 2011

A theoretical investigation has been made for electron acoustic waves propagating in a system of ... more A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions d, initial normalized equilibrium density of low temperature ions l and the ratio of temperatures of low temperature ions to high temperature ions b do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary "blowup" solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth's magnetotail region.

Research paper thumbnail of Solitary, Explosive and Rational Solutions for Nonlinear Electron-acoustic Waves with Non-thermal Electrons

A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmag... more A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called "blowup" solutions in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as terrestrial magnetosphere.

Research paper thumbnail of Solitary, Explosive, Rational and Elliptic Doubly Periodic Solutions for Nonlinear Electron-Acoustic Waves in the Earth’s Magneto tail Region with Cold Electron Fluid and Isothermal Ions

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized c... more A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is used here. Numerical studies have been made using plasma parameters close to those values corresponding to Earth's plasma sheet boundary layer region reveals different solutions i.e., bell-shaped solitary pulses and singularity solutions at a finite point which called "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrass elliptic doubly periodic type solutions, in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as earth's magnetotail region and terrestrial magnetosphere.

Research paper thumbnail of Computational Solutions for the Korteweg–deVries Equation in Warm Plasma

Computational Methods in Science and Technology, 2010

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equatio... more The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters to reveal different solutions, i.e. bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points called "blowup" solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.

Research paper thumbnail of Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

Journal of the Association of Arab Universities for Basic and Applied Sciences, 2014

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Bu... more A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics. ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

Research paper thumbnail of Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

Advances in Mathematical Physics, 2012

The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation ... more The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation for small-but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called "blowup" solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Research paper thumbnail of Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Bu... more A method for solving three types of nonlinear evolution equations namely KdV, modified
KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from
symmetry reduction to space and time variables and similarity reductions for nonlinear evolution
equations are performed. The obtained self-similar solutions of KdV and mKdV equations are
related to Bessel and Airy functions whereas those of Burgers equation are related to the error
and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves.
Also, the method can be applied to other nonlinear evolution equations in mathematical physics.

Research paper thumbnail of Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Bu... more A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics. ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

Research paper thumbnail of Nonlinear ion acoustic waveforms for Kadomstev–Petviashvili equation

The reductive perturbation method has been employed to derive the Kadomstev-Petviashvili equation... more The reductive perturbation method has been employed to derive the Kadomstev-Petviashvili equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation is applied in obtaining a series of solutions of the Kadomstev-Petviashvili equation. Numerical studies have been made using plasma parameters reveals different waveforms such as bell-shaped solitary pulses, rational pulses and others with singularity at finite points which called blowup solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere plasma.

Research paper thumbnail of Solitary, explosive and periodic solutions for electron acoustic solitary waves with non-thermal hot ions

A theoretical investigation has been made for electron acoustic waves propagating in a system of ... more A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions d, initial normalized equilibrium density of low temperature ions l and the ratio of temperatures of low temperature ions to high temperature ions b do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary "blowup" solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth's magnetotail region.

Research paper thumbnail of Computational Solutions for the Korteweg–deVries Equation in Warm Plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equatio... more The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters to reveal different solutions, i.e. bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points called "blowup" solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.

Research paper thumbnail of Solitary, Explosive, Rational and Elliptic Doubly Periodic Solutions for Nonlinear Electron-Acoustic Waves in the Earth’s Magneto tail Region with Cold Electron Fluid and Isothermal Ions

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized c... more A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is used here. Numerical studies have been made using plasma parameters close to those values corresponding to Earth's plasma sheet boundary layer region reveals different solutions i.e., bell-shaped solitary pulses and singularity solutions at a finite point which called "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrass elliptic doubly periodic type solutions, in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as earth's magnetotail region and terrestrial magnetosphere.

Research paper thumbnail of Solitary, explosive and rational solutions for nonlinear electron-acoustic waves with non-thermal electrons

A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmag... more A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called "blowup" solutions in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as terrestrial magnetosphere.

Research paper thumbnail of Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation ... more The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation for small-but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called "blowup" solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Research paper thumbnail of Solitary, explosive and periodic solutions for electron acoustic solitary waves with non-thermal hot ions

Advances in Space Research, 2011

A theoretical investigation has been made for electron acoustic waves propagating in a system of ... more A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions d, initial normalized equilibrium density of low temperature ions l and the ratio of temperatures of low temperature ions to high temperature ions b do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary "blowup" solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth's magnetotail region.

Research paper thumbnail of Solitary, Explosive and Rational Solutions for Nonlinear Electron-acoustic Waves with Non-thermal Electrons

A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmag... more A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called "blowup" solutions in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as terrestrial magnetosphere.

Research paper thumbnail of Solitary, Explosive, Rational and Elliptic Doubly Periodic Solutions for Nonlinear Electron-Acoustic Waves in the Earth’s Magneto tail Region with Cold Electron Fluid and Isothermal Ions

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized c... more A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is used here. Numerical studies have been made using plasma parameters close to those values corresponding to Earth's plasma sheet boundary layer region reveals different solutions i.e., bell-shaped solitary pulses and singularity solutions at a finite point which called "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrass elliptic doubly periodic type solutions, in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as earth's magnetotail region and terrestrial magnetosphere.

Research paper thumbnail of Computational Solutions for the Korteweg–deVries Equation in Warm Plasma

Computational Methods in Science and Technology, 2010

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equatio... more The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters to reveal different solutions, i.e. bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points called "blowup" solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.

Research paper thumbnail of Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

Journal of the Association of Arab Universities for Basic and Applied Sciences, 2014

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Bu... more A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics. ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

Research paper thumbnail of Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

Advances in Mathematical Physics, 2012

The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation ... more The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation for small-but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called "blowup" solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Research paper thumbnail of Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Bu... more A method for solving three types of nonlinear evolution equations namely KdV, modified
KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from
symmetry reduction to space and time variables and similarity reductions for nonlinear evolution
equations are performed. The obtained self-similar solutions of KdV and mKdV equations are
related to Bessel and Airy functions whereas those of Burgers equation are related to the error
and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves.
Also, the method can be applied to other nonlinear evolution equations in mathematical physics.

Research paper thumbnail of Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Bu... more A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics. ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

Research paper thumbnail of Nonlinear ion acoustic waveforms for Kadomstev–Petviashvili equation

The reductive perturbation method has been employed to derive the Kadomstev-Petviashvili equation... more The reductive perturbation method has been employed to derive the Kadomstev-Petviashvili equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation is applied in obtaining a series of solutions of the Kadomstev-Petviashvili equation. Numerical studies have been made using plasma parameters reveals different waveforms such as bell-shaped solitary pulses, rational pulses and others with singularity at finite points which called blowup solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere plasma.

Research paper thumbnail of Solitary, explosive and periodic solutions for electron acoustic solitary waves with non-thermal hot ions

A theoretical investigation has been made for electron acoustic waves propagating in a system of ... more A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions d, initial normalized equilibrium density of low temperature ions l and the ratio of temperatures of low temperature ions to high temperature ions b do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary "blowup" solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth's magnetotail region.

Research paper thumbnail of Computational Solutions for the Korteweg–deVries Equation in Warm Plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equatio... more The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters to reveal different solutions, i.e. bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points called "blowup" solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.

Research paper thumbnail of Solitary, Explosive, Rational and Elliptic Doubly Periodic Solutions for Nonlinear Electron-Acoustic Waves in the Earth’s Magneto tail Region with Cold Electron Fluid and Isothermal Ions

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized c... more A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is used here. Numerical studies have been made using plasma parameters close to those values corresponding to Earth's plasma sheet boundary layer region reveals different solutions i.e., bell-shaped solitary pulses and singularity solutions at a finite point which called "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrass elliptic doubly periodic type solutions, in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as earth's magnetotail region and terrestrial magnetosphere.

Research paper thumbnail of Solitary, explosive and rational solutions for nonlinear electron-acoustic waves with non-thermal electrons

A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmag... more A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called "blowup" solutions in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as terrestrial magnetosphere.

Research paper thumbnail of Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation ... more The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation for small-but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called "blowup" solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.