Travelling-Wave Solution of Volterra Lattice by the Optimal Homotopy Analysis Method

Abstract

The travelling-wave solution of the Volterra lattice has been constructed by the optimal homotopy analysis method. The optimal method used here contains three auxiliary convergence-control parameters to adjust and control the convergence region of the solution. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained, which give much better approximations than those given by the usual homotopy analysis method. The obtained results show that the optimal homotopy analysis method is also very efficient for differential-difference equations.