Long range scattering for higher order Schrodinger operators

被引：6

作者：

Duan, Zhiwen ^{[1
]}

Zheng, Quan ^{[1
]}

Feng, Jing ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 08期

关键词：

Higher order Schrodinger operator; Wave operator; Scattering operator; EQUATIONS; POTENTIALS;

D O I：

10.1016/j.jde.2013.01.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the scattering problem for the higher order Schrodinger operator (-Delta)(m)+V(x), where V(x) is a long-range potential. At this moment the classical wave operators do not exist, so we provide one kind of modified wave operators and show the existence and the asymptotic completeness of such wave operators, as well as the expression of the corresponding scattering operator. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3329 / 3351

页数：23

共 25 条

[1] Scattering in the energy space and below for 3D NLS [J].

Bourgain, J .

JOURNAL D ANALYSE MATHEMATIQUE, 1998, 75 (1) :267-297

[2] Global well-posedness and scattering for the energy-critical nonlinear Schrodinger equation in R3 [J].

Colliander, J. ;

Keel, M. ;

Staffilani, G. ;

Takaoka, H. ;

Tao, T. .

ANNALS OF MATHEMATICS, 2008, 167 (03) :767-865

[3]

FADDEEV LD, 1963, T MIAN, V69

[4]

Ginibre J., 1993, COMMUN MATH PHYS, V151, P615

[5]

Hormander L., 1983, Grundlehren der Mathematischen Wissenschaften, V257

[6]

Hormander L., 1983, ANAL LINEAR PARTIAL

[7]

Hormander L., 1985, ANAL LINEAR PARTIAL, VIV

[8]

Hrmander L., 1985, The analysis of linear partial differential operators III, Pseudodifferential operators

[9] Semilinear Schrodinger flows on hyperbolic spaces: scattering in H1 [J].

Ionescu, Alexandru D. ;

Staffilani, Gigliola .

MATHEMATISCHE ANNALEN, 2009, 345 (01) :133-158

[10]

Kato T., 1966, MATH ANN, V162, P258

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