264 research outputs found
Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation
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.Comment: 28 pages, 2 figure
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