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

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

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)805-813
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume240
Issue number9-10
DOIs
StatePublished - 15 Apr 2011

Keywords

  • Double-well potentials
  • Long range interactions
  • Nonlinear Schrodinger equations

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