Effects of long-range nonlinear interactions in double-well potentials

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Wang, C.¹  Kevrekidis, P. G.¹  Frantzeskakis, D. J.²  Malomed, B. A.³ 

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[2] Univ Athens, Dept Phys, Athens 15784, Greece

[3] Tel Aviv Univ, Fac Engn, Sch Elect Engn, Dept Phys Elect, IL-69978 Tel Aviv, Israel

关键词: Nonlinear Schrodinger equations;    Double-well potentials;    Long range interactions;   

DOI  :  10.1016/j.physd.2010.10.014

来源: Elsevier

【 摘 要 】

We consider the interplay of linear double-well-potential (DWP) structures and nonlinear long-range interactions of different types, motivated by applications to nonlinear optics and matter waves. We find that, while the basic spontaneous-symmetry-breaking (SSB) bifurcation structure in the DWP persists in the presence of the long-range interactions, the critical points at which the SSB emerges are sensitive to the range of the nonlocal interaction. We quantify the dynamics by developing a few-mode approximation corresponding to the DWP structure, and analyze the resulting system of ordinary differential equations and its bifurcations in detail. We compare results of this analysis with those produced by the full partial differential equation, finding good agreement between the two approaches. Effects of the competition between the local self-attraction and nonlocal repulsion on the SSB are studied too. A far more complex bifurcation structure involving the possibility for not only supercritical but also subcritical bifurcations and even bifurcation loops is identified in that case. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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