Application of the exp-function method to nonlinear lattice differential equations for multi-wave and rational solutions

Abstract

In this paper, we extend the basic Exp-function method to nonlinear lattice differential equations for constructing multi-wave and rational solutions for the first time. We consider a differential-difference analogue of the Korteweg-de Vries equation to elucidate the solution procedure. Our approach is direct and unifying in the sense that the bilinear formalism of the equation studied becomes redundant.