An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2008,（9）
• 页码范围: 583-586
• 页数: 4页
• 语种: 英文

摘要

In this paper,to construct exact solution of nonlinear partial differential equation,an easy-to-use approach is proposed.By means of the transformation of the independent variables and the travelling wave transformation,the partial differential equation is reduced to an ordinary differential equation.To solve the ordinary differential equation,we assume the soliton solution in the explicit expression and obtain the travelling wave solution.By the transformation back to the original independent variables,the soliton solution of the original partial differential equation is derived.We investigate the short wave model for the Camassa Holm equation and the Degasperis Procesi equation respectively.One-cusp soliton solution of the Camassa-Holm equation is obtained.One-loop soliton solution of the Degasperis-Procesi equation is also obtained,the approximation of which in a dosed form can be obtained firstly by the Adomian decomposition method.The obtained results in a parametric form coincide perfectly with those given in the present reference.This illustrates the efficiency and reliability of our approach.