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

Yun-Mei Zhao, Ying-Hui He and Yao Long

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/960798

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:960798

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