## Journal of Applied Mathematics

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

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 960798, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808261

Digital Object Identifier
doi:10.1155/2013/960798

Mathematical Reviews number (MathSciNet)
MR3133973

Zentralblatt MATH identifier
06950961

#### Citation

Zhao, Yun-Mei; He, Ying-Hui; Long, Yao. The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations. J. Appl. Math. 2013 (2013), Article ID 960798, 7 pages. doi:10.1155/2013/960798. https://projecteuclid.org/euclid.jam/1394808261

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