Interior inverse problem for global conservative multipeakon solutions of the Camassa-Holm equation

被引：0
作者：
Liu, Tao [1 ]
Lyu, Kang [2 ]
机构：
[1] Shaanxi Normal Univ, Sch Math & Stat, Xian 710062, Peoples R China
[2] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing 210094, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 395卷
关键词：
Interior inverse problem; The Camassa-Holm equation; Weyl-Titchmarsh function; SPECTRAL PROBLEM; ISOSPECTRAL PROBLEM; TRANSFORM; STABILITY;
D O I：
10.1016/j.jde.2024.03.018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the interior inverse problem associated with the global conservative multipeakon solution of the Camassa-Holm equation. Based on the inverse spectral theory on the half-line and the oscillation property of eigenfunctions, some (non)uniqueness results of the interior inverse problem are obtained. In addition, we give the trace formula, which connects the global conservative multipeakon solution with the corresponding eigenvalues and normalized eigenfunctions. (c) 2024 Elsevier Inc. All rights reserved.
引用
收藏
页码：262 / 307
页数：46
相关论文
共 54 条
[1]   Acoustic scattering and the extended Korteweg-de Vries hierarchy [J].
Beals, R ;
Sattinger, DH ;
Szmigielski, J .
ADVANCES IN MATHEMATICS, 1998, 140 (02) :190-206
[2]   Multipeakons and the classical moment problem [J].
Beals, R ;
Sattinger, DH ;
Szmigielski, J .
ADVANCES IN MATHEMATICS, 2000, 154 (02) :229-257
[3]   On the spectral problem associated with the Camassa-Holm equation [J].
Bennewitz, C .
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2004, 11 (04) :422-434
[4]   On solvability of three spectra problem [J].
Boyko, Olga ;
Pivovarchik, Vyacheslav ;
Yang, Chuan Fu .
MATHEMATISCHE NACHRICHTEN, 2016, 289 (14-15) :1727-1738
[5]   Global conservative solutions of the Camassa-Holm equation [J].
Bressan, Alberto ;
Constantin, Adrian .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 183 (02) :215-239
[6]   AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].
CAMASSA, R ;
HOLM, DD .
PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664
[7]  
Camassa R., 1994, Adv. Appl. Mech, V31, P1, DOI DOI 10.1016/S0065-2156(08)70254-0
[8]   Minimizations of positive periodic and Dirichlet eigenvalues for general indefinite Sturm-Liouville problems [J].
Chu, Jifeng ;
Meng, Gang ;
Zhang, Zhi .
ADVANCES IN MATHEMATICS, 2023, 432
[9]   Sharp bounds for Dirichlet eigenvalue ratios of the Camassa-Holm equations [J].
Chu, Jifeng ;
Meng, Gang .
MATHEMATISCHE ANNALEN, 2024, 388 (02) :1205-1224
[10]   Continuous dependence and estimates of eigenvalues for periodic generalized Camassa-Holm equations [J].
Chu, Jifeng ;
Meng, Gang ;
Zhang, Zhi .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (07) :6343-6358
123456