Variational Iteration Method for Solving Nonlinear Differential- Difference Equations

Since the work of Fermi and his co-workers in the 1950s [29], finding exact solutions or good approximations of the nonlinear differentialdifference equations (NDDEs) has played an important role in modeling of complicated physical phenomena such as particle vibrations in lattice, current flows in electrical networks, biophysical systems, molecular crystals and so on. Recently, there have been lots of efforts in giving exact or approximate solutions for NDDEs, for instance, Baldwin algorithm [2], Xie's method [3] and Wu's method [4] which search exact discrete soliton solutions while Wu and his co-workers [5] extended Adomian decomposition method [31] to find the approximate solutions for NDDEs and Wang et al. [6] applied the homotopy analysis method [21] to solve approximately NDDEs. Moreover, Exp-function method which was first introduced by He [32] has been applied by Zhu [22-24] in solving some lattice equations. In 1997, He [7, 8] introduced the variational iteration method which is considered as a modification of the general Lagrange multiplier method [30]. Since then, He's variational iteration method has been applied repeatedly and it has proved to be an effective, simple and accurate method in solving a large class of nonlinear problems [7-18], Applications of the variational iteration method, among other places, may be found in [25-28] and in particular in [13] and their bibliographies. In this paper, we employ the variational iteration method in solving some lattice equations and we obtain approximate soliton solutions for them.