Nonlinear Schrödinger equations with a four-well potential in two dimensions: Bifurcations and stability analysis

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

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schrödinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis.

Original languageEnglish
Title of host publicationNonlinear Science and Complexity
PublisherSpringer Netherlands
Pages173-179
Number of pages7
ISBN (Print)9789048198832
DOIs
StatePublished - 2011
Externally publishedYes

Keywords

  • Double-well potentials
  • Few-mode reduction
  • Linear stability analysis
  • Nonlinear Schrödinger equations

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