Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation

Details Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation

2011-01-27

arxiv.org/abs/1101.5402v1

Nonlinear Sciences

Pattern Formation and Solitons

28 pages, 2 figures

Scientific paper

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.

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