The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations

A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonl...

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Main Authors: Yun-Mei Zhao, Ying-Hui He, Yao Long
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/960798
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author Yun-Mei Zhao
Ying-Hui He
Yao Long
author_facet Yun-Mei Zhao
Ying-Hui He
Yao Long
author_sort Yun-Mei Zhao
collection DOAJ
description A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.
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publishDate 2013-01-01
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series Journal of Applied Mathematics
spelling doaj-art-a2ee6f4f83ca4b4badd9995853c614a62025-08-20T03:38:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/960798960798The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ EquationsYun-Mei Zhao0Ying-Hui He1Yao Long2Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaDepartment of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaDepartment of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaA good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.http://dx.doi.org/10.1155/2013/960798
spellingShingle Yun-Mei Zhao
Ying-Hui He
Yao Long
The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
Journal of Applied Mathematics
title The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
title_full The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
title_fullStr The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
title_full_unstemmed The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
title_short The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
title_sort simplest equation method and its application for solving the nonlinear nlse kgz gds ds and gz equations
url http://dx.doi.org/10.1155/2013/960798
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