Symmetry breaking bifurcation in Nonlinear Schrodinger /Gross-Pitaevskii Equations
Pattern Formation and Solitons
2007-05-23 v1
Abstract
We consider a class of nonlinear Schrodinger / Gross-Pitaveskii (NLS-GP) equations, i.e. NLS with a linear potential. 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. In the special case where the linear potential is a double-well with well separation L, we estimate N_{cr}, the symmetry breaking threshold. Along the ``lowest energy'' symmetric branch, there is an exchange of stability from the symmetric to asymmetric branch as N is increased beyond N_{cr}.
Keywords
Cite
@article{arxiv.nlin/0702038,
title = {Symmetry breaking bifurcation in Nonlinear Schrodinger /Gross-Pitaevskii Equations},
author = {E. W. Kirr and P. G. Kevrekidis and E. Shlizerman and M. I. Weinstein},
journal= {arXiv preprint arXiv:nlin/0702038},
year = {2007}
}
Comments
38 pages, 6 figures