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Papers by emad shewy

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, 2016

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 Rogue waves for Kadomstev-Petviashvili equation in electron-positron-ion plasma

Astrophysics and Space Science, 2014

The nonlinear ion-acoustic waves in plasma having excess super-thermal electrons and positrons ha... more The nonlinear ion-acoustic waves in plasma having excess super-thermal electrons and positrons have been investigated. Reductive perturbation method is used to obtain a Kadomstev-Petviashvili equation describing the system. The dynamics of the modulationally unstable wave packets described by the Kadomstev-Petviashvili equation gives rise to the formation of rogue excitation that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on the system parameters investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as galactic clusters, interstellar medium.

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

Computational Methods in Science and Technology, 2010

Consider a collisionless ionization-free unmagnetized plasma consisting of a mixture of warm ion-... more Consider a collisionless ionization-free unmagnetized plasma consisting of a mixture of warm ion-fluid and iso

Research paper thumbnail of Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

Journal of Theoretical and Applied Physics, 2014

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many n... more The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP equation are constructed.

Research paper thumbnail of New Travelling Wave Solutions for an Asymmetric Model of a Rod in a Lattice Fluid with Nonlinear Advection

Zeitschrift für Naturforschung A, 2006

Based on the modified extended tanh-function method, we consider the continuum problem of the dri... more Based on the modified extended tanh-function method, we consider the continuum problem of the driven diffusive flow of particles behind an impenetrable obstacle (rod) of the length L. The results show that the presence of an obstacle, whether stationary or moving, in a driven diffusive flow with nonlinear drift will distort the local concentration profile to a state which divided the (x,y)-plane into two regions. The concentration is relatively higher in one side than the other side, apart from the value of , where D is the diffusion coefficient and v is the drift velocity. This problem has relevance for the size segregation of particulate matter which results from the relative motion of different-size paricles induced by shaking. The obtained soultions include soliton, periodical, rational and singular solutions.

Research paper thumbnail of Improved dust acoustic solitary waves in two temperature dust fluids

A theoretical investigation is carried out for contribution of the higher-order nonlinearity to n... more A theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear dust-acoustic solitary waves (DASWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Bolltzmannian ions and electrons. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge grains are found to significantly change the higher-order properties (viz. the amplitude and width) of the DASWs.

Research paper thumbnail of Effect of Higher-Order Corrections on the Propagation of Nonlinear Dust-Acoustic Solitary Waves in Mesospheric Dusty Plasmas

Zeitschrift für Naturforschung A, 2006

The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied usin... more The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied using the reductive perturbation method in an unmagnetized collisionless mesospheric dusty plasma. A Korteweg - de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation, and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution is achived via renormalization method

Research paper thumbnail of Space—time fractional KdV—Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

Chinese Physics B, 2014

The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly ... more The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

Research paper thumbnail of Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in 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 electron-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time

Research paper thumbnail of Solution of Time-Fractional Korteweg-de Vries Equation in warm Plasma

Arxiv preprint arXiv: …, 2010

Abstract: The reductive perturbation method has been employed to derive the Korteweg-de Vries (Kd... more Abstract: The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude ion-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular ...

Research paper thumbnail of Dust-ion-acoustic solitons with transverse perturbation

Physics of Plasmas, 2005

The ionization source model is considered, for the first time, to study the combined effects of t... more The ionization source model is considered, for the first time, to study the combined effects of trapped electrons, transverse perturbation, ion streaming velocity, and dust charge fluctuations on the propagation of dust-ion-acoustic solitons in dusty plasmas. The solitary waves are investigated through the derivation of the damped modified Kadomtsev–Petviashivili equation using the reductive perturbation method. Conditions for the formation of solitons as well as their properties are clearly explained. The relevance of our investigation to supernovae shells is also discussed.

Research paper thumbnail of Effect of dust charge fluctuation on the propagation of dust-ion acoustic waves in inhomogeneous mesospheric dusty plasma

Physics of Plasmas, 2008

Investigation of positive and negative dust charge fluctuations on the propagation of dust-ion ac... more Investigation of positive and negative dust charge fluctuations on the propagation of dust-ion acoustic waves (DIAWs) in a weakly inhomogeneous, collisionless, unmagnetized dusty plasmas consisting of cold positive ions, stationary positively and negatively charged dust particles and isothermal electrons. The reductive perturbation method is employed to reduce the basic set of fluid equations to the variable coefficients Korteweg–de Varies (KdV) equation. At the critical ion density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified variable coefficients KdV equation. It is found that the presence of positively charged dust grains does not only significantly modify the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical ion density, neither KdV nor the modified KdV equation is appropriate for describing the DIAWs. The...

Research paper thumbnail of Time-fractional KdV equation for plasma of two different temperature electrons and stationary ion

Physics of Plasmas, 2011

Using the time-fractional KdV equation, the nonlinear properties of small but finite amplitude el... more Using the time-fractional KdV equation, the nonlinear properties of small but finite amplitude electron-acoustic solitary waves are studied in a homogeneous system of unmagnetized collisionless plasma. This plasma consists of cold electrons fluid, non-thermal hot electrons, and stationary ions. Employing the reductive perturbation technique and the Euler-Lagrange equation, the time-fractional KdV equation is derived and it is solved using variational method. It is found that the time-fractional parameter significantly changes the soliton amplitude of the electron-acoustic solitary waves. The results are compared with the structures of the broadband electrostatic noise observed in the dayside auroral zone.

Research paper thumbnail of Contribution of higher order dispersion to nonlinear dust-acoustic solitary waves in dusty plasma with different sized dust grains and nonthermal ions

Physica Scripta, 2008

The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionles... more The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg-de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained.

Research paper thumbnail of Linear and nonlinear properties of electron-acoustic solitary waves with non-thermal electrons

Chaos, Solitons & Fractals, 2007

Propagation of linear and nonlinear electron-acoustic waves (EAWs) in an unmagnetized collisionle... more Propagation of linear and nonlinear electron-acoustic waves (EAWs) in an unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions are investigated. The standard normalmode analysis is used to study the stability condition of linear (EAWs) waves. For nonlinear (EAWs) waves, a reductive perturbation method was employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential. The effects of a non-thermal distribution of hot electrons on the amplitude, width and energy of electrostatic solitary structures are also discussed.

Research paper thumbnail of Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

Astrophysics and Space Science, 2010

... 2008; Abdelwahed et al. ... used for deriving the Korteweg–de Vries (KdV), Zakharov–Kuznetsov... more ... 2008; Abdelwahed et al. ... used for deriving the Korteweg–de Vries (KdV), Zakharov–Kuznetsov (ZK), and Kadomtsev–Petviashvili (KP) equations (Duan 2002; El-Labany et ... The study of the amplitude and width of solitons is a common way to further recognize waves in plasmas. ...

Research paper thumbnail of Time-fractional KdV equation for electron-acoustic waves in plasma of cold electron and two different temperature isothermal ions

Astrophysics and Space Science, 2011

The time fractional KdV equation is derived for small but finite amplitude electron-acoustic soli... more The time fractional KdV equation is derived for small but finite amplitude electron-acoustic solitary waves in plasma of cold electron fluid with two different temperature isothermal ions. The effects of the time fractional parameter on the electrostatic solitary structures are presented. It is shown that the effect of time fractional parameter can be used to modify the amplitude of the

Research paper thumbnail of On the speed and shape of electron acoustic solitary waves

Astrophysics and Space Science, 2012

Electron acoustic solitary waves in a collisionless plasma consisting of a cold electron fluid an... more Electron acoustic solitary waves in a collisionless plasma consisting of a cold electron fluid and nonthermal hot electrons are investigated by a direct analysis of the field equations. The Sagdeev potential is obtained in terms of electron acoustic speed by simply solving an algebraic equation. It is found that the amplitude and width of the electron acoustic solitary waves as well as the parametric regime where the solitons can exist are very sensitive to the population of energetic non-thermal hot electrons. The soliton and double layer solutions are obtained as a small-amplitude approximation. The effect of non-thermal hot electrons is found to significantly change the properties of the electron acoustic solitary waves (EAWs). A comparison with the Viking Satellite observations in the day side auroral zone is also discussed.

Research paper thumbnail of Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

Astrophysics and Space Science, 2013

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogene... more The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth's magnetotail region.

Research paper thumbnail of Ion-acoustic waves in unmagnetized collisionless weakly relativistic plasma of warm-ion and isothermal-electron using time-fractional KdV equation

Advances in Space Research, 2012

ABSTRACT Collisionless unmagnetized plasma consisting of a mixture of warm ion-fluid and isotherm... more ABSTRACT Collisionless unmagnetized plasma consisting of a mixture of warm ion-fluid and isothermal-electron is considered, assuming that the ion flow velocity has a weak relativistic effect. 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 this plasma. The semi-inverse method and Agrawal’s method lead to the Euler–Lagrange equation that leads to the time fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations show that the fractional order may play the same rule of higher order dissipation in KdV equation to modulate the soliton wave amplitude in the plasma system. The results of the present investigation may be applicable to some plasma environments, such as space-plasmas, laser-plasma interaction, plasma sheet boundary layer of the earth’s magnetosphere, solar atmosphere and interplanetary space.

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, 2016

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 Rogue waves for Kadomstev-Petviashvili equation in electron-positron-ion plasma

Astrophysics and Space Science, 2014

The nonlinear ion-acoustic waves in plasma having excess super-thermal electrons and positrons ha... more The nonlinear ion-acoustic waves in plasma having excess super-thermal electrons and positrons have been investigated. Reductive perturbation method is used to obtain a Kadomstev-Petviashvili equation describing the system. The dynamics of the modulationally unstable wave packets described by the Kadomstev-Petviashvili equation gives rise to the formation of rogue excitation that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on the system parameters investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as galactic clusters, interstellar medium.

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

Computational Methods in Science and Technology, 2010

Consider a collisionless ionization-free unmagnetized plasma consisting of a mixture of warm ion-... more Consider a collisionless ionization-free unmagnetized plasma consisting of a mixture of warm ion-fluid and iso

Research paper thumbnail of Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

Journal of Theoretical and Applied Physics, 2014

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many n... more The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP equation are constructed.

Research paper thumbnail of New Travelling Wave Solutions for an Asymmetric Model of a Rod in a Lattice Fluid with Nonlinear Advection

Zeitschrift für Naturforschung A, 2006

Based on the modified extended tanh-function method, we consider the continuum problem of the dri... more Based on the modified extended tanh-function method, we consider the continuum problem of the driven diffusive flow of particles behind an impenetrable obstacle (rod) of the length L. The results show that the presence of an obstacle, whether stationary or moving, in a driven diffusive flow with nonlinear drift will distort the local concentration profile to a state which divided the (x,y)-plane into two regions. The concentration is relatively higher in one side than the other side, apart from the value of , where D is the diffusion coefficient and v is the drift velocity. This problem has relevance for the size segregation of particulate matter which results from the relative motion of different-size paricles induced by shaking. The obtained soultions include soliton, periodical, rational and singular solutions.

Research paper thumbnail of Improved dust acoustic solitary waves in two temperature dust fluids

A theoretical investigation is carried out for contribution of the higher-order nonlinearity to n... more A theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear dust-acoustic solitary waves (DASWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Bolltzmannian ions and electrons. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge grains are found to significantly change the higher-order properties (viz. the amplitude and width) of the DASWs.

Research paper thumbnail of Effect of Higher-Order Corrections on the Propagation of Nonlinear Dust-Acoustic Solitary Waves in Mesospheric Dusty Plasmas

Zeitschrift für Naturforschung A, 2006

The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied usin... more The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied using the reductive perturbation method in an unmagnetized collisionless mesospheric dusty plasma. A Korteweg - de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation, and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution is achived via renormalization method

Research paper thumbnail of Space—time fractional KdV—Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

Chinese Physics B, 2014

The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly ... more The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

Research paper thumbnail of Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in 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 electron-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time

Research paper thumbnail of Solution of Time-Fractional Korteweg-de Vries Equation in warm Plasma

Arxiv preprint arXiv: …, 2010

Abstract: The reductive perturbation method has been employed to derive the Korteweg-de Vries (Kd... more Abstract: The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude ion-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular ...

Research paper thumbnail of Dust-ion-acoustic solitons with transverse perturbation

Physics of Plasmas, 2005

The ionization source model is considered, for the first time, to study the combined effects of t... more The ionization source model is considered, for the first time, to study the combined effects of trapped electrons, transverse perturbation, ion streaming velocity, and dust charge fluctuations on the propagation of dust-ion-acoustic solitons in dusty plasmas. The solitary waves are investigated through the derivation of the damped modified Kadomtsev–Petviashivili equation using the reductive perturbation method. Conditions for the formation of solitons as well as their properties are clearly explained. The relevance of our investigation to supernovae shells is also discussed.

Research paper thumbnail of Effect of dust charge fluctuation on the propagation of dust-ion acoustic waves in inhomogeneous mesospheric dusty plasma

Physics of Plasmas, 2008

Investigation of positive and negative dust charge fluctuations on the propagation of dust-ion ac... more Investigation of positive and negative dust charge fluctuations on the propagation of dust-ion acoustic waves (DIAWs) in a weakly inhomogeneous, collisionless, unmagnetized dusty plasmas consisting of cold positive ions, stationary positively and negatively charged dust particles and isothermal electrons. The reductive perturbation method is employed to reduce the basic set of fluid equations to the variable coefficients Korteweg–de Varies (KdV) equation. At the critical ion density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified variable coefficients KdV equation. It is found that the presence of positively charged dust grains does not only significantly modify the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical ion density, neither KdV nor the modified KdV equation is appropriate for describing the DIAWs. The...

Research paper thumbnail of Time-fractional KdV equation for plasma of two different temperature electrons and stationary ion

Physics of Plasmas, 2011

Using the time-fractional KdV equation, the nonlinear properties of small but finite amplitude el... more Using the time-fractional KdV equation, the nonlinear properties of small but finite amplitude electron-acoustic solitary waves are studied in a homogeneous system of unmagnetized collisionless plasma. This plasma consists of cold electrons fluid, non-thermal hot electrons, and stationary ions. Employing the reductive perturbation technique and the Euler-Lagrange equation, the time-fractional KdV equation is derived and it is solved using variational method. It is found that the time-fractional parameter significantly changes the soliton amplitude of the electron-acoustic solitary waves. The results are compared with the structures of the broadband electrostatic noise observed in the dayside auroral zone.

Research paper thumbnail of Contribution of higher order dispersion to nonlinear dust-acoustic solitary waves in dusty plasma with different sized dust grains and nonthermal ions

Physica Scripta, 2008

The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionles... more The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg-de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained.

Research paper thumbnail of Linear and nonlinear properties of electron-acoustic solitary waves with non-thermal electrons

Chaos, Solitons & Fractals, 2007

Propagation of linear and nonlinear electron-acoustic waves (EAWs) in an unmagnetized collisionle... more Propagation of linear and nonlinear electron-acoustic waves (EAWs) in an unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions are investigated. The standard normalmode analysis is used to study the stability condition of linear (EAWs) waves. For nonlinear (EAWs) waves, a reductive perturbation method was employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential. The effects of a non-thermal distribution of hot electrons on the amplitude, width and energy of electrostatic solitary structures are also discussed.

Research paper thumbnail of Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

Astrophysics and Space Science, 2010

... 2008; Abdelwahed et al. ... used for deriving the Korteweg–de Vries (KdV), Zakharov–Kuznetsov... more ... 2008; Abdelwahed et al. ... used for deriving the Korteweg–de Vries (KdV), Zakharov–Kuznetsov (ZK), and Kadomtsev–Petviashvili (KP) equations (Duan 2002; El-Labany et ... The study of the amplitude and width of solitons is a common way to further recognize waves in plasmas. ...

Research paper thumbnail of Time-fractional KdV equation for electron-acoustic waves in plasma of cold electron and two different temperature isothermal ions

Astrophysics and Space Science, 2011

The time fractional KdV equation is derived for small but finite amplitude electron-acoustic soli... more The time fractional KdV equation is derived for small but finite amplitude electron-acoustic solitary waves in plasma of cold electron fluid with two different temperature isothermal ions. The effects of the time fractional parameter on the electrostatic solitary structures are presented. It is shown that the effect of time fractional parameter can be used to modify the amplitude of the

Research paper thumbnail of On the speed and shape of electron acoustic solitary waves

Astrophysics and Space Science, 2012

Electron acoustic solitary waves in a collisionless plasma consisting of a cold electron fluid an... more Electron acoustic solitary waves in a collisionless plasma consisting of a cold electron fluid and nonthermal hot electrons are investigated by a direct analysis of the field equations. The Sagdeev potential is obtained in terms of electron acoustic speed by simply solving an algebraic equation. It is found that the amplitude and width of the electron acoustic solitary waves as well as the parametric regime where the solitons can exist are very sensitive to the population of energetic non-thermal hot electrons. The soliton and double layer solutions are obtained as a small-amplitude approximation. The effect of non-thermal hot electrons is found to significantly change the properties of the electron acoustic solitary waves (EAWs). A comparison with the Viking Satellite observations in the day side auroral zone is also discussed.

Research paper thumbnail of Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

Astrophysics and Space Science, 2013

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogene... more The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth's magnetotail region.

Research paper thumbnail of Ion-acoustic waves in unmagnetized collisionless weakly relativistic plasma of warm-ion and isothermal-electron using time-fractional KdV equation

Advances in Space Research, 2012

ABSTRACT Collisionless unmagnetized plasma consisting of a mixture of warm ion-fluid and isotherm... more ABSTRACT Collisionless unmagnetized plasma consisting of a mixture of warm ion-fluid and isothermal-electron is considered, assuming that the ion flow velocity has a weak relativistic effect. 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 this plasma. The semi-inverse method and Agrawal’s method lead to the Euler–Lagrange equation that leads to the time fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations show that the fractional order may play the same rule of higher order dissipation in KdV equation to modulate the soliton wave amplitude in the plasma system. The results of the present investigation may be applicable to some plasma environments, such as space-plasmas, laser-plasma interaction, plasma sheet boundary layer of the earth’s magnetosphere, solar atmosphere and interplanetary space.