Homoclinic orbits and localized solutions in discrete nonlinear Schrodinger equation with long-range interaction

Abstract

In this paper, we use the homoclinic orbit approach without using small perturbations to prove the existence of soliton solutions of the discrete nonlinear Schr¨odinger equations with long-range interaction by employing the properties of the symmetries of reversible planar maps. Moreover, the long-range interaction by a potential is proportional to 1/l1+α with fractional α < 1 and l as natural number.