Journal of Mathematical Research and Applications
The Modified Simple Equation Method Applied to Nonlinear Two Models of DiffusionReaction Equations 

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Abstract: 

In this paper, we employ the modified simple equation method (MSEM) to find the exact solutions of some nonlinear partial differential equations (PDEs), namely two different models of nonlinear diffusion reaction equations arising in many physical problems and including one dimensional turbulence, sound and shock waves in viscous medium etc. The applicability of this method for constructing these exact solutions is demonstrated. This paper is qualified because finding the exact solutions for these two nonlinear equations is difficult. The MSEM is useful to find the exact solutions of nonlinear evolution reaction diffusion equations in mathematical physics and engineering problems. These solutions are kink and antikink shaped soliton solutions. 

Keywords:Nonlinear DiffusionReaction Equations; Modified Simple Equation Method; Traveling Wave Solutions; Exact Solutions; Solitary Wave Solution 

Author: Elsayed M. E. Zayed^{1}  1.Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt 

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