STABILITY IN THE ENERGY SPACE FOR CHAINS OF SOLITONS OF THE ONE-DIMENSIONAL GROSS-PITAEVSKII EQUATION

被引：14

作者：

Bethuel, Fabrice ^{[1
]}

Gravejat, Philippe ^{[2
]}

Smets, Didier ^{[1
]}

机构：

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

[2] Ecole Polytech, Ctr Math Laurent Schwartz, F-91128 Palaiseau, France

来源：

ANNALES DE L INSTITUT FOURIER | 2014年 / 64卷 / 01期

关键词：

Gross-Pitaevskii equation; sums of solitons; stability; NONLINEAR SCHRODINGER-EQUATION; TRAVELING-WAVES; SOLITARY WAVES; GKDV EQUATIONS; CAUCHY-PROBLEM; SUM;

D O I：

10.5802/aif.2838

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and spatially ordered according to their speeds.

引用

页码：19 / 70

页数：52

共 22 条

[11] Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation [J].

Gerard, Patrick ;

Zhang, Zhifei .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2009, 91 (02) :178-210

[12] 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

[13]

Lin Z., 2002, Adv. Differential Equations, V47, P897

[14] Stability in H1 of the sum of K solitary waves for some nonlinear Schrodinger equations [J].

Martel, Y ;

Merle, F ;

Tsai, TP .

DUKE MATHEMATICAL JOURNAL, 2006, 133 (03) :405-466

[15] Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations [J].

Martel, Y ;

Merle, F ;

Tsai, TP .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 231 (02) :347-373

[16] Inelastic interaction of nearly equal solitons for the quartic gKdV equation [J].

Martel, Yvan ;

Merle, Frank .

INVENTIONES MATHEMATICAE, 2011, 183 (03) :563-648

[17] Stability of Two Soliton Collision for Nonintegrable gKdV Equations [J].

Martel, Yvan ;

Merle, Frank .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 286 (01) :39-79

[18] KORTEWEG-DEVRIES EQUATION - SURVEY OF RESULTS [J].

MIURA, RM .

SIAM REVIEW, 1976, 18 (03) :412-459

[19]

Tartousi H., THESIS

[20] Long-time asymptotics of solutions to the Cauchy problem for the defocusing nonlinear Schrodinger equation with finite-density initial data. II. Dark solitons on continua [J].

Vartanian, AH .

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2002, 5 (04) :319-413

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