Scattering theory and self-similar solutions for the nonlinear Schrodinger equation

被引：18
|
作者：
Cazenave, T
Weissler, FB
机构：
[1] Univ Paris 06, CNRS, UMR 7598, F-75252 Paris 05, France
[2] Univ Paris 13, Inst Galilee, Lab Anal Geometrie & Applicat, CNRS,UMR 7539, F-93430 Villetaneuse, France
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2000年 / 31卷 / 03期
关键词：
nonlinear Schrodinger equation; self-similar solution; scattering theory;
D O I：
10.1137/S0036141099351309
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a certain class of mild solutions of the nonlinear Schrodinger equation iu(t) + Delta u = gamma\u\(alpha)u. In particular, we develop a scattering theory in this class of solutions. As a consequence, we characterize self-similar solutions in Lalpha+2 whose gradient is in L-2. In addition, we prove the existence of classical H-1 global solutions having various specified rates of decay as t --> infinity.
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页码：625 / 650
页数：26
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