THE "GOOD" BOUSSINESQ EQUATION: LONG-TIME ASYMPTOTICS

被引：42

作者：

Charlier, Christophe ^{[1
]}

Lenells, Jonatan ^{[1
]}

Wang, Deng-Shan ^{[2
]}

机构：

[1] KTH Royal Inst Technol, Dept Math, Stockholm, Sweden

[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing, Peoples R China

来源：

ANALYSIS & PDE | 2023年 / 16卷 / 06期

基金：

中国国家自然科学基金; 欧洲研究理事会; 瑞典研究理事会;

关键词：

asymptotics; Boussinesq equation; Riemann-Hilbert problem; inverse scattering transform; initial value problem; RIEMANN-HILBERT PROBLEMS; STEEPEST DESCENT METHOD; GLOBAL EXISTENCE; BEHAVIOR; SCATTERING; LIMIT; NLS;

D O I：

10.2140/apde.2023.16.1351

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial-value problem for the "good" Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a 3 x 3-matrix Riemann- Hilbert problem. We establish formulas for the long-time asymptotics of the solution by performing a Deift-Zhou steepest descent analysis of a regularized version of this Riemann-Hilbert problem. Our results are valid for generic solitonless Schwartz class solutions whose space-average remains bounded as t -> infinity.

引用

页码：1351 / 1388

页数：39

共 34 条

[1] GLOBAL EXISTENCE OF SMOOTH SOLUTIONS AND STABILITY OF SOLITARY WAVES FOR A GENERALIZED BOUSSINESQ EQUATION [J].

BONA, JL ;

SACHS, RL .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 118 (01) :15-29

[2] Long time asymptotic behavior of the focusing nonlinear Schrodinger equation [J].

Borghese, Michael ;

Jenkins, Robert ;

McLaughlin, Kenneth D. T-R .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35 (04) :887-920

[3]

Boussinesq J., 1872, J. Math. Pures Appl., V17, P55

[4]

Charlier C, 2022, INDIANA U MATH J, V71, P1505

[5] Long-time asymptotics for the pure radiation solution of the Sine-Gordon equation [J].

Cheng, PJ ;

Venakides, S ;

Zhou, X .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (7-8) :1195-1262

[6] Well-posedness and nonlinear smoothing for the "good" Boussinesq equation on the half-line [J].

Compaan, E. ;

Tzirakis, N. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (12) :5824-5859

[7]

De Monvel AB, 2019, ANN I FOURIER, V69, P171

[8] LONG-TIME ASYMPTOTICS FOR THE CAMASSA-HOLM EQUATION [J].

De Monvel, Anne Boutet ;

Kostenko, Aleksey ;

Shepelsky, Dmitry ;

Teschl, Gerald .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2009, 41 (04) :1559-1588

[9] A STEEPEST DESCENT METHOD FOR OSCILLATORY RIEMANN-HILBERT PROBLEMS - ASYMPTOTICS FOR THE MKDV EQUATION [J].

DEIFT, P ;

ZHOU, X .

ANNALS OF MATHEMATICS, 1993, 137 (02) :295-368

[10] Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space [J].

Deift, P ;

Zhou, X .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2003, 56 (08) :1029-1077

← 1 2 3 4 →