Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices

TL;DR

This paper constructs explicit localized and periodic solutions to the nonlinear Schrödinger equation with spatially modulated linear and nonlinear potentials, analyzing their properties and implications for stabilizing gap solitons in periodic lattices.

Contribution

It introduces a method to derive explicit solutions for the nonlinear Schrödinger equation with spatially varying parameters, enhancing understanding of soliton stabilization in modulated lattices.

Findings

Explicit localized and periodic solutions are derived.

The solutions' properties and stability are analyzed.

Implications for gap soliton stabilization are discussed.

Abstract

Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.