Exact Traveling Wave Solutions Of Certain Nonlinear Partial Differential Equations Using The (G0=G2)-Expansion Method

Abstract

In this thesis, G0=G2-expansion Method was implemented in solving nonlinear partial differential equation of (1+1)-dimensional Ito equation(mathematical finance equaton) and (1+1)-dimensional combined Kdv and Mkdv equation. The G0=G2-expansion method was applied based on two different methods, namely (G0=G) and (1=G)-expansion methods. These two different methods are applied on (1+1)-dimensional Ito equation and (1+1)-dimensional combined Kdv and Mkdv equation solved for three different cases Posative, Negative and zero and the exact solution of Nonlinear partial differential equation of (1+1)-dimensional Ito equation and (1+1)-dimensional combined Kdv and Mkdv equation is obtained. From the obtained results two of them were illustrated by graphical plots. Further, the obtained results are fits with solutions which solves the complicity of finding the solutions for NLPDEs. Finally the method is best and effective method to solve NLPDEs