On nonlinear Schrodinger type equations with nonlinear damping
Résumé
We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which we describe. We also prove that the presence of a quadratic confinement in at least one spatial direction is sufficient to ensure that the solution of our model decays to zero for large time. In the case without external potential we prove that the solution may not go to zero for large time due to (non-trivial) scattering.
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