Spatial properties and numerical solitary waves of a nonintegrable discrete nonlinear Schrödinger equation with nonlinear hopping

Abstract

In this paper, we study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with nonlinear hopping. By using the planar nonlinear dynamical map approach, we address the spatial properties of the nonintegrable dNLS equation. Through the constructions of exact period-1 and period-2 orbits of a planar nonlinear map which is a stationary version of the nonintegrable dNLS equation, we obtain the spatially periodic solutions of the nonintegrable dNLS equation. We also give the numerical simulations of the orbits of the planar nonlinear map and show how the nonlinear hopping terms affect those orbits. By using discrete Fourier transformation method, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation.