Application of He’s Variational Iteration Method and Adomian Decomposition Method to Solution for the Fifth Order Caudrey-Dodd-Gibbon (CDG) Equation

The theory of solitary waves has attracted much interest in recent years for treatment of PDEs describing nonlinear and evolution concepts. Nonlinear phenomena appear in many areas of scientific fields such as solid state physics, plasma physics, fluid dynamics, mathematical biology and chemical kinetics. The nonlinear problems are characterized by dispersive effects, dissipative effects, convection-advection, and diffusion process. A broad class of analytical solutions methods, such as inverse scattering method, Ba ̈cklund transformation method, Hirota’s bilinear scheme [1-6], Hereman’s method [7,8], pseudo spectral method, Jacobi elliptic method, Painleve ́ analysis [9], and other methods, were used to handle these problems. However, some of these analytical solutions methods are not easy to use because of the tedious work that it requires. This paper is concerned with the multiple-soliton solutions of the fifth order nonlinear Caudrey-Dodd-Gibbon (CDG) equation [10,11]