Title

Bose-Einstein Condensates And Multi-Component Nls Models On Symmetric Spaces Of Bd.I-Type. Expansions Over Squared Solutions

Keywords

Generalized Fourier transform; Inverse scattering method; Multicomponent nonlinear Schrödinger equations

Abstract

A special class of multicomponent NLS equations, generalizing the vector NLS and related to the BD.I-type symmetric are shown to be integrable through the inverse scattering method (ISM). The corresponding fundamental analytic solutions are constructed thus reducing the inverse scattering problem to a Riemann-Hilbert problem. We introduce the minimal sets of scattering data which determines uniquely the scattering matrix and the potential Q of the Lax operator. The elements of can be viewed as the expansion coefficients of Q over the 'squared solutions' that are natural generalizations of the standard exponentials. Thus we demonstrate that the mapping is a generalized Fourier transform. Special attention is paid to two special representatives of this MNLS with three-component and five components which describe spinor (F=1 and F=2, respectively) Bose-Einstein condensates. © 2011 Springer Science+Business Media B.V.

Publication Date

12-1-2011

Publication Title

Nonlinear Science and Complexity

Number of Pages

181-188

Document Type

Article; Book Chapter

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-90-481-9884-9_23

Socpus ID

84895235978 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84895235978

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