Rapidly decaying solutions of the nonlinear Schrödinger equation

Abstract

We consider global solutions of the nonlinear Schrδdinger equation

Changing blow-up time in nonlinear Schrödinger equations

“…In particular, they are spread out for positive times, which suggests that in a nonlinear setting, such oscillations may prevent wave collapse. The intuition described on the last two cases is confirmed by the results of Cazenave and Weissler [12].…”

“…It is shown in [12] that if the initial datum u 0 , such that (1.2) holds, is replaced by u 0 (x)e −ib|x| 2 with b > 0 sufficiently large, then the blow-up time is anticipated (and is O(b −1 )). On the other hand, if u 0 is replaced by u 0 (x)e ib|x| 2 with b > 0 sufficiently large, then no blow-up occurs.…”

On small amplitude solutions to the generalized Boussinesq equations

“…The critical exponent γ(n) naturally arises in the problem of the existence of small amplitude solutions decaying as O(|t| [6,15,31,35,36] for instance). This paper is organized as follow.…”

Wave Operators for the Coupled Klein-Gordon-Schrödinger Equations in Two Space Dimensions

“…There are amount of papers concerning the asymptotic behavior of solutions for the nonlinear Schrö dinger equation (see [3,6,9,10,11,12,14,17,18,22,24,25,26,27,35,36,37,38,39,40,41]), and for the nonlinear Klein-Gordon equation (see [4,5,13,20,19,21,23,24,28,30,34,35,36,37]). We consider the existence of wave operators W G .…”