Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

TL;DR

This paper investigates the existence and stability of self-trapped localized states, such as gap solitons and nonlinear Bloch waves, in optical and matter-wave media with combined linear and nonlinear periodic potentials, revealing conditions for their stability.

Contribution

It demonstrates that nonlinear lattice potentials can stabilize certain localized states that are unstable in constant nonlinearity settings, combining properties of linear and nonlinear lattices.

Findings

Gap solitons are stable inside a single nonlinear lattice well.

Nonlinear Bloch waves can be stabilized by nonlinear lattices.

The study discusses experimental realization possibilities.

Abstract

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity, supported by a combination of linear and nonlinear periodic lattice potentials. The former is found to be stable once placed inside a single well of the nonlinear lattice, it is unstable otherwise. Contrary to the case with constant self-focusing nonlinearity, where the latter solution is always unstable, here, we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices. The practical possibilities for experimental realization of the predicted solutions are also discussed.