A Riccati Equation Approach and Travelling Wave Solutions for Nonlinear Evolution Equations

In this paper, a new method, called Riccati equation approach, is proposed to seek travelling wave solutions of nonlinear evolution equations. The quasilinear Klein–Gordon equation and the KdV equation are chosen to illustrate the effectiveness and convenience of the suggested method. The obtained solutions which include solitons, kinks and periodic solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The study highlights the power and the effectiveness of the proposed method which can be used in a direct way to handle many other nonlinear evolution equations. © 2015, Springer India Pvt. Ltd.