Perturbation theory for calculating solitary waves in one-dimensional lattices

Abstract

A systematic method is given to compute solitary waves in one-dimensional lattices. The procedure, based on perturbation theory, leads to an infinite series, which has to be summed up completely. This can be done by the use of Pade approximation or a pseudo-potential method. We obtain exact results in the case of the Toda lattice and good approximations for solitary waves in non-integrable systems. For the Toda lattice also theN-soliton solution is calculated.