Symmetry-breaking bifurcation in nonlinear schrödinger/gross- pitaevskii equations

E. W. Kirr, P. G. Kevrekidis, E. Shlizerman, M. I. Weinstein

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a class of nonlinear Schrödinger/Gross-Pitaeveskii (NLS-GP) equations, i.e., NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear optical as well as macroscopic quantum phenomena (BEC). We obtain conditions for a symmetry-breaking bifurcation in a symmetric family of states as M, the squared L 2 norm (particle number, optical power), is increased. The bifurcating asymmetric state is a "mixed mode" which, near the bifurcation point, is approximately a superposition of symmetric and antisymmetric modes. In the special case where the linear potential is a double well with well-separation L, we estimate N cr(L), the symmetry breaking threshold. Along the "lowest energy" symmetric branch, there is an exchange of stability from the symmetric to the asymmetric branch as N is increased beyond N cr.

Original languageEnglish (US)
Pages (from-to)566-604
Number of pages39
JournalSIAM Journal on Mathematical Analysis
Volume40
Issue number2
DOIs
StatePublished - 2008

Keywords

  • Bound state
  • Gross-Pitaevskii
  • Nonlinear schrodinger
  • Soliton

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Symmetry-breaking bifurcation in nonlinear schrödinger/gross- pitaevskii equations'. Together they form a unique fingerprint.

Cite this