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

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.

nonlinear Schrodinger equation, double-well potentials, symmetric and asymmetric stationary states, pitchfork bifurcations, stability, normal form