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Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system

Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system In this paper Lie symmetry analysis method is applied to study nonlinear generalized Zakharov system which is the coupled nonlinear system of Schrödinger equations. With the aid of Lie point symmetry, nonlinear generalized Zakharov system is reduced into the ODEs and some group invariant solutions are obtained where some solutions are new, which are not reported in literatures. Then the bifurcation theory and qualitative theory are employed to investigate nonlinear generalized Zakharov system. Through the analysis of phase portraits, some Jacobi-elliptic function solutions are found, such as the periodic-wave solutions, kink-shaped and bell-shaped solitary-wave solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-017-0200-x
Publisher site
See Article on Publisher Site

Abstract

In this paper Lie symmetry analysis method is applied to study nonlinear generalized Zakharov system which is the coupled nonlinear system of Schrödinger equations. With the aid of Lie point symmetry, nonlinear generalized Zakharov system is reduced into the ODEs and some group invariant solutions are obtained where some solutions are new, which are not reported in literatures. Then the bifurcation theory and qualitative theory are employed to investigate nonlinear generalized Zakharov system. Through the analysis of phase portraits, some Jacobi-elliptic function solutions are found, such as the periodic-wave solutions, kink-shaped and bell-shaped solitary-wave solutions.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Nov 8, 2017

References