Nonlinear Schrodinger equation with a harmonic potential
Codes used to find ground states for the NLS with a harmonic potential (Gross-Pitaevskii equation). Ground states are found from the shooting method that enables to track down solutions of the BVP from the solutions of an IVP by shooting with the value of the spectral parameter. We consider a different range of power nonlinearities and subcritical, critical, and supercritical dimensions.
In the energy-critical and energy-supercritical cases we also plot the dependecies of the spectral parameter on the L-infinity norm of ground states.
For the energy-supercritical case, we estimate Morse indices of the linearized operators, where we linearized either about the ground state, or the limiting singular solution.