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Miniature of Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation
Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation

Date: 2006-04-01

Creator: R. Carretero-González, J. D. Talley, C. Chong, B. A. Malomed

Access: Open access

We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities. We produce a stability diagram for different families of soliton solutions that suggests the (co)existence of infinitely many branches of stable localized solutions. Bifurcations that occur with an increase in the coupling constant are studied in a numerical form. A variational approximation is developed for accurate prediction of the most fundamental and next-order solitons, together with their bifurcations. Salient properties of the model, which distinguish it from the well-known cubic DNLS equation, are the existence of two different types of symmetric solitons and stable asymmetric soliton solutions that are found in narrow regions of the parameter space. The asymmetric solutions appear from and disappear back into the symmetric ones via loops of forward and backward pitchfork bifurcations. © 2006 Elsevier Ltd. All rights reserved.
Miniature of Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices
Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices

Date: 2009-01-15

Creator: C. Chong, R. Carretero-González, B. A. Malomed, P. G. Kevrekidis

Access: Open access

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.