The "Good" Boussinesq Equation: a Riemann-Hilbert Approach

被引：0
|
作者：
Charlier, Christophe [1 ]
Lenells, Jonatan [1 ]
机构：
[1] KTH Royal Inst Technol, S-10044 Stockholm, Sweden
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2022年 / 71卷 / 04期
基金：
瑞典研究理事会; 欧洲研究理事会;
关键词：
Spectral analysis; Boussinesq equation; Riemann-Hilbert problem; inverse scattering transform; initial value problem; INVERSE SCATTERING;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop an inverse scattering transform formalism for the "good " Boussinesq equation on the line. Assuming that the solution exists, we show that it can be expressed in terms of the solution of a 3 x 3 matrix Riemann-Hilbert problem. The Riemann-Hilbert problem is formulated in terms of two reflection coefficients whose definitions involve only the initial data, and it has a form which makes it suitable for the evaluation of long-time asymptotics via Deift-Zhou steepest descent arguments.
引用
收藏
页码：1505 / 1562
页数：58
相关论文
共 50 条
  • [1] A Riemann-Hilbert Approach for the Novikov Equation
    Boutet De Monvel, Anne
    Shepelsky, Dmitry
    Zielinski, Lech
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2016, 12
  • [2] A Riemann-Hilbert approach to the Laplace equation
    Fokas, AS
    Kapaev, AA
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 251 (02) : 770 - 804
  • [3] A Riemann-Hilbert Approach to the Heun Equation
    Dubrovin, Boris
    Kapaev, Andrei
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2018, 14
  • [4] The short pulse equation by a Riemann-Hilbert approach
    de Monvel, Anne Boutet
    Shepelsky, Dmitry
    Zielinski, Lech
    LETTERS IN MATHEMATICAL PHYSICS, 2017, 107 (07) : 1345 - 1373
  • [5] Riemann-Hilbert Approach to the Elastodynamic Equation: Part I
    Its, Alexander
    Its, Elizabeth
    Kaplunov, Julius
    LETTERS IN MATHEMATICAL PHYSICS, 2011, 96 (1-3) : 53 - 83
  • [6] A Riemann-Hilbert approach for the Degasperis-Procesi equation
    de Monvel, Anne Boutet
    Shepelsky, Dmitry
    NONLINEARITY, 2013, 26 (07) : 2081 - 2107
  • [7] The Ostrovsky-Vakhnenko equation: A Riemann-Hilbert approach
    de Monvel, Anne Boutet
    Shepelsky, Dmitry
    COMPTES RENDUS MATHEMATIQUE, 2014, 352 (03) : 189 - 195
  • [8] The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach
    de Monvel, Anne Boutet
    Shepelsky, Dmitry
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2015, 48 (03)
  • [9] A Riemann-Hilbert approach for the modified short pulse equation
    Guo, Boling
    Liu, Nan
    APPLICABLE ANALYSIS, 2019, 98 (09) : 1646 - 1659
  • [10] Riemann-Hilbert approach to the elastodynamic equation: half plane
    Its, Alexander
    Its, Elizabeth
    LETTERS IN MATHEMATICAL PHYSICS, 2021, 111 (03)
12345