A novel (G'/G)-expansion method and its application to the Boussinesq equation

In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.

A simple approach to solving double sinh–Gordon equation

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation abundant types of explicit and exact solutions for the double sinh-Gordon equation are derived in a simple manner.

New Types of Travelling Wave Solutions From （2＋l）-Dimensional Davey-Stewartson Equation

In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixtb-aegree nonnneal term, we study the （2＋l ）-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.

A new method to the(2+1)-dimensional modified KP equation

By means of the auxiliary ordinary differential equation method,we have obtained many solitary wave solutions,periodic wave solutions and variable separation solutions for the (2+1)-dimensional KP equation.Using a mixed method,many exact solutions have been obtained.