Finite time extinction by nonlinear damping for the Schrodinger equation

Next, we show that when the nonlinear object is a non-degenerate state or a degen- erate excited state satisfying a simplicity condition, the convergence holds for all positive

The method of proof involves the generalization of previous works on supercritical NLS and gKdV equations by Martel, Merle and the first author [3] to the wave case, where we

This is the reason why we presented here some new results on the general theory of the existence, uniqueness and regularity of solutions of the strongly damped Schr¨ odinger

If the initial data have the critical size, then at leading order the wave function propagates like a coherent state whose envelope is given by a nonlinear equation, up to a time of

This is the reason why we presented here some new results on the general theory of the existence, uniqueness and regularity of solutions of the strongly damped Schr¨odinger

Malomed, Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity, J. Tsutsumi, Scattering problem for nonlinear Schr¨ odinger equations,

Key Words: damped Schr¨ odinger equation, existence, uniqueness, finite time extinction, asymptotic behavior... The literature is too extensive to give an

In the super-critical case, the WKB analy- sis provides a new phenomenon for the (classical) cubic, defocusing nonlinear Schr¨ odinger equation, which can be compared to the loss