D.E. Pelinovsky and T. Phan
Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation
J. Differential Equations 253 (2012) 2796–2824
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 timedependent
solutions of the nonlinear Schrödinger equation over
long but finite time intervals.
Keywords:
nonlinear Schrodinger equation, double-well potentials,
symmetric and asymmetric stationary states, pitchfork bifurcations, stability, normal form