Construction of exact solutions to the modified forms of DP and CH equations by analytical methods

Abstract

In this work, we establish the exact solutions to the modified forms of Degasperis-Procesi (DP) and Camassa-Holm (CH) equations. The generalized (G'/G)-expansion and generalized tanh-coth methods were used to construct solitary wave solutions of nonlinear evolution equations. The generalized (G'/G)-expansion method presents a wider applicability for handling nonlinear wave equations. It is shown that the (G'/G)-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.