Study of Nonlinear Evolution Equations to Construct Traveling Wave Solutions via Modified Simple Equation Method
Published: 2013-07-18
Page: 490-503
Issue: 2013 - Volume 3 [Issue 4]
Md. Tanjir Ahmed
Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh
Kamruzzaman Khan *
Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh
M. Ali Akbar
Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh
*Author to whom correspondence should be addressed.
Abstract
In this paper, the modified simple equation (MSE) method is executed to find the traveling wave solutions for the (2+1)-dimensional modified KdV–Kadomtsev–Petviashvili (mKdV-KP) equation and the (2+1)-dimensional Painlevé integrable Burgers equation (PIB). The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It has shown that the method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations.
Keywords: MSE method, nonlinear evolution equations (NLEEs), mKdV-KP equation, Painlevé integrable Burgers (PIB) equation, solitary wave solutions, traveling wave solutions