Solitary Wave Solution Of The Nonlinear Evolution Equation By Adomian Method

As one of the most important partial differential equations, Nonlinear Evolution Equation, with its'wide physical background and particular property, plays a very important role in current scientific development. In this paper, we have studied the application of Adomian method in the Nonlinear Evolution Equation. At first, we briefly introduce the research background of solitary wave solution. Besides, we summarize the traditional resolution to analytic solitary wave solution. Secondly, we give a detailed illustration of the Adomian decomposition method and present it's relation with other approximation methods such as Homotopy Analysis Method etc. Finally, we make an introduction to the convergence theorem of the Adomian method. Then we study several nonlinear evolution equations, for example, Chaffee-Infante equation and nonlinear coupled Schrodinger equation. Numerical experiment and error analysis prove the efficiency of Adomian method in solving the solitary wave solution of the Nonlinear Evolution Equation.