SYMMETRY-BREAKING BIFURCATION IN NONLINEAR SCHRODINGER/GROSS-PITAEVSKII EQUATIONS

被引：60

作者：

Kirr, E. W. ^{[1
]}

Kevrekidis, P. G. ^{[2
]}

Shlizerman, E. ^{[3
]}

Weinstein, M. I. ^{[4
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[3] Weizmann Inst Sci, Dept Appl Math & Comp Sci, IL-76100 Rehovot, Israel

[4] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2008年 / 40卷 / 02期

基金：

美国国家科学基金会;

关键词：

nonlinear Schrodinger; Gross-Pitaevskii; soliton; bound state;

D O I：

10.1137/060678427

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of nonlinear Schrodinger/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 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 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 Ncr.

引用

页码：566 / 604

页数：39

共 35 条

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