scholarly journals Exact solutions of nonlinear evolution equations by using the modified simple equation method

2012 ◽  
Vol 3 (3) ◽  
pp. 321-325 ◽  
Author(s):  
N. Taghizadeh ◽  
M. Mirzazadeh ◽  
A. Samiei Paghaleh ◽  
J. Vahidi
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Simple Equation ◽  
Equation Method ◽  
Modified Simple Equation Method

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

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yun-Mei Zhao ◽  
Ying-Hui He ◽  
Yao Long
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Simplest Equation Method ◽  
Klein Gordon ◽  
Schrödinger's Equation ◽  
Wave Reduction

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.

scholarly journals Traveling-Wave Solution of Modified Liouville Equation by Means of Modified Simple Equation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Md. Abdus Salam
Keyword(s):  
Liouville Equation ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Nonlinear Evolution Equations ◽  
Simple Equation ◽  
Equation Method ◽  
New Approach ◽  
Modified Simple Equation Method

We construct the traveling wave solutions involving parameters of modified Liouville equation by using a new approach, namely the modified simple equation method. The proposed method is direct, concise, and elementary and can be used for many other nonlinear evolution equations.

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