Existence and stability of discrete solitons in nonlinear Schrödinger lattices with hard potentials

Abstract

In this paper we study the discrete solitons in nonlinear Schrödinger lattices with hard potentials. We first derive some sufficient conditions for the existence of discrete solitons in the anti-continuum limit. We then establish some spectral stability and instability results for discrete solitons in the anti-continuum limit using the regular perturbation theory. We also develop asymptotic approximations of the eigenvalues of the linearized stability problem.