Symmetry-Breaking Bifurcation in the Nonlinear Schrödinger Equation with Symmetric Potentials

E. Kirr, P. G. Kevrekidis, D. E. Pelinovsky

Research output: Contribution to journalArticle

Abstract

We consider the focusing (attractive) nonlinear Schrödinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either a subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the ground states at both small and large values for the corresponding eigenvalue parameter.

Original languageEnglish (US)
Pages (from-to)795-844
Number of pages50
JournalCommunications in Mathematical Physics
Volume308
Issue number3
DOIs
StatePublished - Dec 1 2011

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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