Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices

TL;DR

This paper investigates the existence, stability, and mobility of multistable discrete solitons in 2D and 3D nonlinear Schroedinger lattices with cubic-quintic nonlinearities, revealing new hybrid soliton species and mobility limitations.

Contribution

It introduces hybrid solitons in higher-dimensional lattices and analyzes their bifurcations, stability, and mobility, extending understanding beyond 1D models.

Findings

Discovery of hybrid solitons unique to 2D and 3D lattices.

Bifurcation analysis of stationary solutions.

Mobility of solitons limited by radiation loss and Peierls-Nabarro barrier.

Abstract

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately crafted Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.