Vector nonlinear Klein-Gordon lattices: General derivation of small amplitude envelope soliton solutions

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

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Topological and Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger and the Coupled Quadratic Nonlinear Equations

Quantum Physics Letters ◽

10.12785/qpl/030101 ◽

2014 ◽

Vol 3 (1) ◽

pp. 1-5 ◽

Cited By ~ 2

Author(s):

Mozhgan Akbari

Keyword(s):

Nonlinear Equations ◽

Soliton Solutions ◽

Topological Soliton ◽

Klein Gordon

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On global small amplitude solutions to systems of cubic nonlinear Klein–Gordon equations with different mass terms in one space dimension

Journal of Differential Equations ◽

10.1016/s0022-0396(03)00125-6 ◽

2003 ◽

Vol 192 (2) ◽

pp. 308-325 ◽

Cited By ~ 34

Author(s):

Hideaki Sunagawa

Keyword(s):

Small Amplitude ◽

Space Dimension ◽

Klein Gordon ◽

Mass Terms ◽

One Space Dimension

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Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

Journal of Applied Mathematics ◽

10.1155/2013/972416 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 8

Author(s):

Ming Song ◽

Bouthina S. Ahmed ◽

Anjan Biswas

Keyword(s):

Finite Difference ◽

Numerical Simulations ◽

Power Law ◽

Soliton Solution ◽

Bifurcation Analysis ◽

Soliton Solutions ◽

Phase Portraits ◽

Zakharov Equation ◽

Topological Soliton ◽

Klein Gordon

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

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Properties of Alfvén Solitons in a Finite-Beta Plasma J. Plasma Phys. vol. 27, 1982, p. 193

Journal of Plasma Physics ◽

10.1017/s0022377800002099 ◽

1984 ◽

Vol 32 (2) ◽

pp. 347-347 ◽

Cited By ~ 1

Author(s):

Steven R. Spangler ◽

James P. Sheerin

Keyword(s):

Soliton Solutions ◽

Alfven Waves ◽

Plasma Phys ◽

Alfvén Waves ◽

Envelope Soliton ◽

Translational Invariance ◽

Non Linear ◽

Image Position

In the aforementioned paper we obtained an equation for non-linear Alfvén waves in a finite-β plasma, and investigated envelope soliton solutions thereof. The purpose of this note is to point out an error in the derivation of the soliton envelopes, and present corrected expressions for these solitons.The error arises from our assumption of translational invariance of both the envelope and phase of an envelope soliton expressed in equations (16) and (17). Rather, the phase is related to the amplitude by where y ≡ x — VEt is a comoving co-ordinate, and all other quantities are defined in the above paper.

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INTEGRABLE ASPECTS AND SOLITON-LIKE SOLUTIONS OF AN INHOMOGENEOUS COUPLED HIROTA–MAXWELL–BLOCH SYSTEM IN OPTICAL FIBERS WITH SYMBOLIC COMPUTATION

Modern Physics Letters A ◽

10.1142/s0217732310032688 ◽

2010 ◽

Vol 25 (16) ◽

pp. 1365-1381 ◽

Cited By ~ 1

Author(s):

YU-SHAN XUE ◽

BO TIAN ◽

HAI-QIANG ZHANG ◽

LI-LI LI

Keyword(s):

Symbolic Computation ◽

Optical Fibers ◽

Soliton Solutions ◽

Graphical Analysis ◽

Envelope Soliton ◽

Fiber Communication ◽

Erbium Doped ◽

Higher Order Dispersion ◽

Interaction Behaviors ◽

Soliton Excitation

For describing wave propagation in an inhomogeneous erbium-doped nonlinear fiber with higher-order dispersion and self-steepening, an inhomogeneous coupled Hirota–Maxwell–Bloch system is considered with the aid of symbolic computation. Through Painlevé singularity structure analysis, the integrable condition of such a system is analyzed. Via the Painlevé-integrable condition, the Lax pair is explicitly constructed based on the Ablowitz–Kaup–Newell–Segur scheme. Furthermore, the analytic soliton-like solutions are obtained via the Darboux transformation which makes it exercisable to generate the multi-soliton solutions in a recursive manner. Through the graphical analysis of some obtained analytic one- and two-soliton-like solutions, our concerns are mainly on the envelope soliton excitation, the propagation features of optical solitons and their interaction behaviors in actual fiber communication. Finally, the conservation laws for the system are also presented.

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