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

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. Copyright © 2011 John Wiley & Sons, Ltd.