Exact solutions of space-time dependent Korteweg-de Vries equation by the extended unified method

Abstract

Recently the unified method for finding traveling wave solutions of nonlinear evolution equations was proposed by one of the authors. It was shown that, this method unifies all the methods being used to find these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg-de Vries (KdV) equation with space-time dependent coefficients. A new class of multiple-soliton or wave trains is obtained.