Long time dynamics near the symmetry breaking bifurcation for Nonlinear Schrödinger/Gross-Pitaevskii Equations

Long time dynamics near the symmetry breaking bifurcation for Nonlinear Schrödinger/Gross-Pitaevskii Equations

With Michael Weinstein, we show long time stability of specific oscillatory solutions to an inhomogeneous nonlinear Schrödinger equation with a double well potential. The solutions arerelated to classical orbits from a finite dimension system of ODE's.
In particular, we show the oscillations persist in the infinite dimensional system over several periods in an asymptotic setting.