Direct gradient flow for defocusing action ground states of rotating nonlinear Schrödinger equations is unconditionally stable and converges globally and locally exponentially under non-degeneracy assumptions.
Fukuizumi, Stability and instability of standing waves for the nonline ar Schr¨ odinger equation with harmonic potential , Discrete Contin
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Analysis of gradient flow for computing defocusing action ground states of rotating nonlinear Schr\"odinger equations
Direct gradient flow for defocusing action ground states of rotating nonlinear Schrödinger equations is unconditionally stable and converges globally and locally exponentially under non-degeneracy assumptions.