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Scattering for nonlinear Schrodinger equation under partial harmonic confinement
Paolo Antonelli, Rémi Carles, Jorge Drumond Silva
We consider the nonlinear Schrodinger equation under a partial quadratic confinement. We show that the global dispersion corresponding to the direction(s) with no potential is enou…
Large time behavior in nonlinear Schrodinger equation with time dependent potential
Rémi Carles, Jorge Drumond Silva
We consider the large time behavior of solutions to defocusing nonlinear Schrodinger equation in the presence of a time dependent external potential. The main assumption on the pot…
Higher order Schrodinger and Hartree-Fock equations
Remi Carles, Wolfgang Lucha, Emmanuel Moulay
The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-o…
On nonlinear Schrodinger type equations with nonlinear damping
Paolo Antonelli, Rémi Carles, Christof Sparber
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 w…