Sharp asymptotic behavior of solutions for cubic nonlinear Schrodinger equations with a potential

被引：49
作者：
Naumkin, I. P. [1 ,2 ]
机构：
[1] Univ Paris 06, BC 187,4 Pl Jussieu, F-75252 Paris 05, France
[2] CNRS, Lab Jacques Louis Lions, BC 187,4 Pl Jussieu, F-75252 Paris 05, France
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 05期
关键词：
LONG-RANGE SCATTERING; INVERSE SCATTERING; LARGE TIME; ENERGY; SPACE; OPERATORS; WAVES; LIGHT;
D O I：
10.1063/1.4948743
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the cubic nonlinear Schrodinger equation with a potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions to the Cauchy problem. Published by AIP Publishing.
引用
收藏
页数：31
相关论文
共 40 条
[1]  
[Anonymous], 2003, SOBOLEV SPACES
[2]   Scattering for Nonlinear Schrodinger Equation Under Partial Harmonic Confinement [J].
Antonelli, Paolo ;
Carles, Remi ;
Silva, Jorge Drumond .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 334 (01) :367-396
[3]   PERTURBATION METHOD FOR A NONLINEAR WAVE MODULATION .2. [J].
ASANO, N ;
TANIUTI, T ;
YAJIMA, N .
JOURNAL OF MATHEMATICAL PHYSICS, 1969, 10 (11) :2020-&
[4]   NONEXISTENCE OF ASYMPTOTICALLY FREE SOLUTIONS FOR A NONLINEAR SCHRODINGER-EQUATION [J].
BARAB, JE .
JOURNAL OF MATHEMATICAL PHYSICS, 1984, 25 (11) :3270-3273
[5]   PROPAGATION OF NONLINEAR WAVE ENVELOPES [J].
BENNEY, DJ ;
NEWELL, AC .
JOURNAL OF MATHEMATICS AND PHYSICS, 1967, 46 (02) :133-&
[6]   Wave collapse in physics: principles and applications to light and plasma waves [J].
Berge, L .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1998, 303 (5-6) :259-370
[7]  
BESPALOV VI, 1966, JETP LETT-USSR, V3, P307
[8]   LARGE TIME BEHAVIOR IN NONLINEAR SCHRODINGER EQUATIONS WITH TIME DEPENDENT POTENTIAL [J].
Carles, Remi ;
Silva, Jorge Drumond .
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2015, 13 (02) :443-460
[9]   NONLINEAR SCHRODINGER EQUATION WITH TIME DEPENDENT POTENTIAL [J].
Carles, Remi .
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2011, 9 (04) :937-964
[10]   RAPIDLY DECAYING SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION [J].
CAZENAVE, T ;
WEISSLER, FB .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 147 (01) :75-100
1234