Coding of nonlinear states for the Gross-Pitaevskii equation with periodic potential

PHYSICA D-NONLINEAR PHENOMENA

卷:254

Article

Alfimov, G. L.¹  Avramenko, A. I.¹ 

[1] Natl Res Univ Elect Technol, Moscow 124498, Russia

关键词: Gross-Pitaevskii equation;    Nonlinear Schrodinger equation;    Nonlinear states;    Coding;   

DOI  :  10.1016/j.physd.2013.03.009

来源: Elsevier

【 摘 要 】

We study nonlinear states for the NLS-type equation with additional periodic potential U(x), also called the Gross-Pitaevskii equation, GPE, in theory of Bose-Einstein Condensate, BEC. We prove that if the nonlinearity is defocusing (repulsive, in the BEC context) then under some conditions there exists a homeomorphism between the set of all nonlinear states for GPE (i.e. real bounded solutions of some nonlinear ODE) and the set of bi-infinite sequences of numbers from 1 to N for some integer N. These sequences can be viewed as codes of the nonlinear states. We present numerical arguments that for GPE with cosine potential these conditions hold in certain areas of the plane of the external parameters. This implies that for these values of parameters all the nonlinear states can be described in terms of the coding sequences. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free