Homoclinic orbits and localized solutions in nonlinear Schrödinger lattices

Abstract

By using the symmetry properties of the reversible planar maps, instead of the Melnikov analysis, we improve the homoclinic orbit approach without assuming small perturbations to prove rigorously the existence of bright and dark soliton solutions of the discrete nonlinear Schrödinger equations with various nonlinearities in one-dimensional lattices. Our approach is valid both for small and large coupling constants. The latter case is inaccessible to the anti-integrability method.