Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger 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 defined Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss. © 2008 Elsevier B.V. All rights reserved.
Chong, C.; Carretero-González, R.; Malomed, B. A.; and Kevrekidis, P. G., "Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices" (2009). Mathematics Faculty Publications. 29.