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Papers by Gro Hovhannisyan

Monthly Notices of the Royal Astronomical Society: Letters, Jul 7, 2021

Axisymmetric magnetohydrodynamic (MHD) models are useful in studies of magnetised winds and nonli... more Axisymmetric magnetohydrodynamic (MHD) models are useful in studies of magnetised winds and nonlinear Alfvén waves in solar and stellar atmospheres. We demonstrate that a condition often used in these models for the determination of a nearly vertical magnetic field is applicable to a radial field instead. A general divergencefree condition in curvilinear coordinates is self-consistently derived and used to obtain the correct condition for the variation of a nearly vertical magnetic field. The obtained general divergence-free condition along with the transfield equation complete the set of MHD equations in curvilinear coordinates for axisymmetric motions and could be useful in studies of magnetised stellar winds and nonlinear Alfvén waves.

The paper establishes local asymptotic representations for solutions of linear singular hyperboli... more The paper establishes local asymptotic representations for solutions of linear singular hyperbolic equations by means of Fourier integral operators. It is assumed that the coecients of the equations are unbounded near a singular hyperplane t = 0. These representations generalize the well known Levinson’s asymptotic theorem from the theory of ordinary dierential equations. They are useful for the study of some equations of mathematical physics. Another application is in the study of correctness of Cauchy problem for the partial dierential equations with multiple characteristics.

Journal of Mathematical Physics

We derive a general time scale version of the Hirota–Miwa equation as a compatibility condition a... more We derive a general time scale version of the Hirota–Miwa equation as a compatibility condition arising from a new version of a three-dimensional Lax system, construct its 3-soliton solutions, and consider various examples. We prove the invariance of the compatibility condition of the two-dimensional Lax system under a gauge transformation. The 3-soliton solution obtained here may be used in modeling in view of its variable graininess and a large number of free parameters.

Electronic Journal of Differential Equations, 2007

We establish error estimates for first-order linear systems of equations and linear second-order ... more We establish error estimates for first-order linear systems of equations and linear second-order dynamic equations on time scales by using calculus on a time scales [1,4,5] and Birkhoff-Levinson's method of asymptotic solutions [3,6,8,9].

Abstract. We establish error estimates for first-order linear systems of equa-tions and linear se... more Abstract. We establish error estimates for first-order linear systems of equa-tions and linear second-order dynamic equations on time scales by using cal-culus on a time scales [1, 4, 5] and Birkhoff-Levinson’s method of asymptotic solutions [3, 6, 8, 9]. 1. Results Asymptotic behavior of solutions of dynamic equations and systems on time scales was investigated in [5]. In this paper we establish error estimates of such asymptotic representations, which may be applied to the investigation of stability of dynamic equations (see f.e. [9]). Consider the system of ordinary differential equations on time scales a∆(t) = A(t)a(t), t> T, (1.1) where a ∆ is delta (Hilger) derivative, a(t) is a n-vector function, and A(t) is a n×n matrix function from Crd(T,∞) (definition of rd-continuous functions see in [4]). A time scale is an arbitrary nonempty closed subset of the real numbers. Let T be a time scale. For t ∈ T we define the forward jump operator σ: T → T by σ(t) = inf{s ∈ T: s> t}....

We consider the Cauchy problem for second and third order linear differential equations with cons... more We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymp-totic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

Eprint Arxiv Physics 0207117, Jul 1, 2002

We introduce notions of free energy and loss in linear, absorbing dielectric media which are rele... more We introduce notions of free energy and loss in linear, absorbing dielectric media which are relevant to the regime in which the macroscopic Maxwell equations are themselves relevant. As such we solve a problem eluded to by Landau and Lifshitz [1] in 1958, and later considered explicitly by Barash and Ginzburg [2], and Oughtsun and Sherman [3]. As such we provide physically-relevant real-time notions of "energy" and "loss" in all analogous linear dissipative systems.

Ultra-Wideband, Short-Pulse Electromagnetics 6, 2003

We establish error estimates for first-order linear systems of equa- tions and linear second-orde... more We establish error estimates for first-order linear systems of equa- tions and linear second-order dynamic equations on time scales by using cal- culus on a time scales (1, 4, 5) and Birkho-Levinson'

We prove asymptotical stability and instability results for a gen- eral second-order dierential e... more We prove asymptotical stability and instability results for a gen- eral second-order dierential equations with complex-valued functions as coef- ficients. To prove asymptotic stability of linear second-order dierential equa- tions, we use the technique of asymptotic representations of solutions and error estimates. For nonlinear second-order dierential equations, we extend the as- ymptotic stability theorem of Pucci and Serrin to the case of complex-valued coecients. 1. Main Results Consider the linear second-order dierential equation

We prove asymptotical stability and instability theorems for 2 × 2 system of firstorder linear dy... more We prove asymptotical stability and instability theorems for 2 × 2 system of firstorder linear dynamic equations on a time scale with complex-valued functions as coefficients. To prove stability estimates and asymptotic stability for a 2 × 2 system we use the integral representations of the fundamental matrix via asymptotic solutions, the error estimates, and the time scales calculus. AMS subject classification: 34A45, 39A11.

We consider the Cauchy problem for second and third order linear dierential equations with consta... more We consider the Cauchy problem for second and third order linear dierential equations with constant complex coecients. We describe neces- sary and sucient conditions on the data for the existence of oscillatory solu- tions. It is known that in the case of real coecients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymp- totic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

We are concerned with the asymptotic behavior of solutions of an n- th order linear dynamic equat... more We are concerned with the asymptotic behavior of solutions of an n- th order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior of the so-called (rst) principal solution in terms of the Taylor monomial of degree n 1: Several interesting properties of the Taylor monomials are established so that we can prove our main results.

Communications in Applied Analysis, 2012

Journal of Mathematical Physics

From the Lax system on a time-space scale, we derive Sine-Gordon, Burgers, and some other nonline... more From the Lax system on a time-space scale, we derive Sine-Gordon, Burgers, and some other nonlinear equations. From the simplified twoand three-dimensional Lax systems on a time-space scale with variable nonvanishing graininess, we derive Korteweg-de Vries, Boussinesq, Krichever-Novikov, Hirota-Miwa, and other nonlinear equations on a time-space scale with soliton solutions. We also construct multisoliton solutions for some equations by the direct method using the exponential functions on a time-space scale.

Journal of Mathematical Physics

Journal of Mathematical Physics

Hirota's direct method is extended on a variable time-space scale. Using this extension, we const... more Hirota's direct method is extended on a variable time-space scale. Using this extension, we construct 3-soliton solutions of the Sine-Gordon equation on a variable space scale. The determinant form of this solution is given as well.

Monthly Notices of the Royal Astronomical Society: Letters, Jul 7, 2021

Axisymmetric magnetohydrodynamic (MHD) models are useful in studies of magnetised winds and nonli... more Axisymmetric magnetohydrodynamic (MHD) models are useful in studies of magnetised winds and nonlinear Alfvén waves in solar and stellar atmospheres. We demonstrate that a condition often used in these models for the determination of a nearly vertical magnetic field is applicable to a radial field instead. A general divergencefree condition in curvilinear coordinates is self-consistently derived and used to obtain the correct condition for the variation of a nearly vertical magnetic field. The obtained general divergence-free condition along with the transfield equation complete the set of MHD equations in curvilinear coordinates for axisymmetric motions and could be useful in studies of magnetised stellar winds and nonlinear Alfvén waves.

The paper establishes local asymptotic representations for solutions of linear singular hyperboli... more The paper establishes local asymptotic representations for solutions of linear singular hyperbolic equations by means of Fourier integral operators. It is assumed that the coecients of the equations are unbounded near a singular hyperplane t = 0. These representations generalize the well known Levinson’s asymptotic theorem from the theory of ordinary dierential equations. They are useful for the study of some equations of mathematical physics. Another application is in the study of correctness of Cauchy problem for the partial dierential equations with multiple characteristics.

Journal of Mathematical Physics

We derive a general time scale version of the Hirota–Miwa equation as a compatibility condition a... more We derive a general time scale version of the Hirota–Miwa equation as a compatibility condition arising from a new version of a three-dimensional Lax system, construct its 3-soliton solutions, and consider various examples. We prove the invariance of the compatibility condition of the two-dimensional Lax system under a gauge transformation. The 3-soliton solution obtained here may be used in modeling in view of its variable graininess and a large number of free parameters.

Electronic Journal of Differential Equations, 2007

We establish error estimates for first-order linear systems of equations and linear second-order ... more We establish error estimates for first-order linear systems of equations and linear second-order dynamic equations on time scales by using calculus on a time scales [1,4,5] and Birkhoff-Levinson's method of asymptotic solutions [3,6,8,9].

Abstract. We establish error estimates for first-order linear systems of equa-tions and linear se... more Abstract. We establish error estimates for first-order linear systems of equa-tions and linear second-order dynamic equations on time scales by using cal-culus on a time scales [1, 4, 5] and Birkhoff-Levinson’s method of asymptotic solutions [3, 6, 8, 9]. 1. Results Asymptotic behavior of solutions of dynamic equations and systems on time scales was investigated in [5]. In this paper we establish error estimates of such asymptotic representations, which may be applied to the investigation of stability of dynamic equations (see f.e. [9]). Consider the system of ordinary differential equations on time scales a∆(t) = A(t)a(t), t> T, (1.1) where a ∆ is delta (Hilger) derivative, a(t) is a n-vector function, and A(t) is a n×n matrix function from Crd(T,∞) (definition of rd-continuous functions see in [4]). A time scale is an arbitrary nonempty closed subset of the real numbers. Let T be a time scale. For t ∈ T we define the forward jump operator σ: T → T by σ(t) = inf{s ∈ T: s> t}....

We consider the Cauchy problem for second and third order linear differential equations with cons... more We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymp-totic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

Eprint Arxiv Physics 0207117, Jul 1, 2002

We introduce notions of free energy and loss in linear, absorbing dielectric media which are rele... more We introduce notions of free energy and loss in linear, absorbing dielectric media which are relevant to the regime in which the macroscopic Maxwell equations are themselves relevant. As such we solve a problem eluded to by Landau and Lifshitz [1] in 1958, and later considered explicitly by Barash and Ginzburg [2], and Oughtsun and Sherman [3]. As such we provide physically-relevant real-time notions of "energy" and "loss" in all analogous linear dissipative systems.

Ultra-Wideband, Short-Pulse Electromagnetics 6, 2003

We establish error estimates for first-order linear systems of equa- tions and linear second-orde... more We establish error estimates for first-order linear systems of equa- tions and linear second-order dynamic equations on time scales by using cal- culus on a time scales (1, 4, 5) and Birkho-Levinson'

We prove asymptotical stability and instability results for a gen- eral second-order dierential e... more We prove asymptotical stability and instability results for a gen- eral second-order dierential equations with complex-valued functions as coef- ficients. To prove asymptotic stability of linear second-order dierential equa- tions, we use the technique of asymptotic representations of solutions and error estimates. For nonlinear second-order dierential equations, we extend the as- ymptotic stability theorem of Pucci and Serrin to the case of complex-valued coecients. 1. Main Results Consider the linear second-order dierential equation

We prove asymptotical stability and instability theorems for 2 × 2 system of firstorder linear dy... more We prove asymptotical stability and instability theorems for 2 × 2 system of firstorder linear dynamic equations on a time scale with complex-valued functions as coefficients. To prove stability estimates and asymptotic stability for a 2 × 2 system we use the integral representations of the fundamental matrix via asymptotic solutions, the error estimates, and the time scales calculus. AMS subject classification: 34A45, 39A11.

We consider the Cauchy problem for second and third order linear dierential equations with consta... more We consider the Cauchy problem for second and third order linear dierential equations with constant complex coecients. We describe neces- sary and sucient conditions on the data for the existence of oscillatory solu- tions. It is known that in the case of real coecients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymp- totic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

We are concerned with the asymptotic behavior of solutions of an n- th order linear dynamic equat... more We are concerned with the asymptotic behavior of solutions of an n- th order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior of the so-called (rst) principal solution in terms of the Taylor monomial of degree n 1: Several interesting properties of the Taylor monomials are established so that we can prove our main results.

Communications in Applied Analysis, 2012

Journal of Mathematical Physics

From the Lax system on a time-space scale, we derive Sine-Gordon, Burgers, and some other nonline... more From the Lax system on a time-space scale, we derive Sine-Gordon, Burgers, and some other nonlinear equations. From the simplified twoand three-dimensional Lax systems on a time-space scale with variable nonvanishing graininess, we derive Korteweg-de Vries, Boussinesq, Krichever-Novikov, Hirota-Miwa, and other nonlinear equations on a time-space scale with soliton solutions. We also construct multisoliton solutions for some equations by the direct method using the exponential functions on a time-space scale.

Journal of Mathematical Physics

Journal of Mathematical Physics

Hirota's direct method is extended on a variable time-space scale. Using this extension, we const... more Hirota's direct method is extended on a variable time-space scale. Using this extension, we construct 3-soliton solutions of the Sine-Gordon equation on a variable space scale. The determinant form of this solution is given as well.