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SYMMETRY-BREAKING BIFURCATION IN NONLINEAR SCHRODINGER/GROSS-PITAEVSKII EQUATIONS
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
  • EW Kirr
  • PG Kevrekidis, University of Massachusetts - Amherst
  • E Shlizerman
  • MI Weinstein
Publication Date
2008
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 ${\cal N}$, 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 ${\cal N}_{cr}(L)$, the symmetry breaking threshold. Along the “lowest energy” symmetric branch, there is an exchange of stability from the symmetric to the asymmetric branch as ${\cal N}$ is increased beyond ${\cal N}_{cr}$.
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJMAAH000040000002000566000001&idtype=cvips&gifs=yes
Pages
566-604
Citation Information
EW Kirr, PG Kevrekidis, E Shlizerman and MI Weinstein. "SYMMETRY-BREAKING BIFURCATION IN NONLINEAR SCHRODINGER/GROSS-PITAEVSKII EQUATIONS" SIAM JOURNAL ON MATHEMATICAL ANALYSIS Vol. 40 Iss. 2 (2008)
Available at: http://works.bepress.com/panos_kevrekidis/136/