MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS. (14th August 2015) - HANI, ZAHER; PAUSADER, BENOIT; TZVETKOV, NIKOLAY; VISCIGLIA, NICOLA
Abstract : We consider the cubic nonlinear Schrödinger equation posed on the spatial domain R× T^d . We prove modified scattering and construct modified wave operators for small initial and final data respectively ( 1d4 ). The key novelty comes from the fact that the modified asymptotic dynamics are dictated by the resonant system of this equation, which sustains interesting dynamics when d2 . As a consequence, we obtain global strong solutions (for d2 ) with infinitely growing high Sobolev norms H^s .