On the KP I Transonic Limit of Two-Dimensional Gross-Pitaevskii Travelling Waves

被引：17

作者：

Bethuel, Fabrice ^{[1
]}

Gravejat, Philippe ^{[2
]}

Saut, Jean-Claude ^{[3
]}

机构：

[1] Univ Paris 06, Lab Jacques Louis Lions, F-75252 Paris 05, France

[2] Univ Paris 09, Ctr Rech Math Decis, F-75775 Paris 16, France

[3] Univ Paris 11, Math Lab, F-91405 Orsay, France

来源：

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 5卷 / 03期

关键词：

Transonic limit; Kadomtsev-Petviashvili equation; Gross-Pitaevskii equation; travelling waves;

D O I：

10.4310/DPDE.2008.v5.n3.a3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a rigorous mathematical derivation of the convergence in the long-wave transonic limit of the minimizing travelling waves for the two-dimensional Gross-Pitaevskii equation towards ground states for the Kadomtsev-Petviashvili equation (KP I).

引用

页码：241 / 280

页数：40

共 28 条

[1] EVOLUTION OF PACKETS OF WATER-WAVES [J].

ABLOWITZ, MJ ;

SEGUR, H .

JOURNAL OF FLUID MECHANICS, 1979, 92 (JUN) :691-715

[2]

Bethuel F, 2004, J EUR MATH SOC, V6, P17

[3]

Bethuel F, 1999, ANN I H POINCARE-PHY, V70, P147

[4]

BETHUEL F, 2008, CONT MATH

[5]

BETHUEL F, 2008, INDIANA U M IN PRESS

[6]

BETHUEL F, 2008, COMMUN MATH IN PRESS

[7] Travelling waves for the Gross-Pitaevskii equation in dimension larger than two [J].

Chiron, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 58 (1-2) :175-204

[8] Nonlinear Schrodinger equation and superfluid hydrodynamics [J].

Coste, C .

EUROPEAN PHYSICAL JOURNAL B, 1998, 1 (02) :245-253

[9]

de Bouard A., 1996, CONT MATH, V200, P75, DOI 10.1090/conm/200/02510

[10] Solitary waves of generalized Kadomtsev-Petviashvili equations [J].

deBouard, A ;

Saut, JC .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02) :211-236

← 1 2 3 →