Stability of solitary waves for derivative nonlinear Schrodinger equation

被引：61

作者：

Colin, Mathieu ^{[1
]}

Ohta, Masahito

机构：

[1] Univ Bordeaux 1, Cours Liberat 451, F-33405 Talence, France

[2] Saitama Univ, Fac Sci, Dept Math, Urawa, Saitama 3388570, Japan

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2006年 / 23卷 / 05期

关键词：

solitary wave; orbital stability; DNLS;

D O I：

10.1016/j.anihpc.2005.09.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the so-called Derivative Nonlinear Schrodinger equation. This equation is known to have a two-parameter family of solitary waves solutions. We prove orbital stability of these particular solutions for the whole range of parameters values by using variational methods. (c) 2006 Elsevier SAS. All rights reserved.

引用

页码：753 / 764

页数：12

共 27 条

[1]

BERESTYCKI H, 1981, CR ACAD SCI I-MATH, V293, P489

[2] Ill-posedness for the derivative Schrodinger and generalized Benjamin-Ono equations [J].

Biagioni, HA ;

Linares, F .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (09) :3649-3659

[3]

Boling G, 1995, J DIFFER EQUATIONS, V123, P35

[4] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].

BREZIS, H ;

LIEB, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490

[5] ORBITAL STABILITY OF STANDING WAVES FOR SOME NON-LINEAR SCHRODING EQUATIONS [J].

CAZENAVE, T ;

LIONS, PL .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 85 (04) :549-561

[6]

Cazenave T., 2003, Semilinear Schrodinger equations, V10

[7] STABILITY OF COULOMB-SYSTEMS WITH MAGNETIC-FIELDS .1. THE ONE-ELECTRON ATOM [J].

FROHLICH, J ;

LIEB, EH ;

LOSS, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 104 (02) :251-270

[8] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .2. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 94 (02) :308-348

[9] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .1. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 74 (01) :160-197

[10] ON THE DERIVATIVE NONLINEAR SCHRODINGER-EQUATION [J].

HAYASHI, N ;

OZAWA, T .

PHYSICA D, 1992, 55 (1-2) :14-36

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