Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation
Pattern Formation and Solitons
2011-01-31 v1
Abstract
We derive and justify a normal form reduction of the nonlinear Schrodinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential. We prove persistence of normal form dynamics for both supercritical and subcritical pitchfork bifurcations in the time-dependent solutions of the nonlinear Schrodinger equation over long but finite time intervals.
Keywords
Cite
@article{arxiv.1101.5402,
title = {Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation},
author = {Dmitry Pelinovsky and Tuoc Phan},
journal= {arXiv preprint arXiv:1101.5402},
year = {2011}
}
Comments
28 pages, 2 figures