On the cauchy problem for an integrable equation with peakon solutions

被引：229
|
作者：
Yin, ZY [1 ]
机构：
[1] Zhongshan Univ, Dept Math, Guangzhou 510275, Peoples R China
来源：
ILLINOIS JOURNAL OF MATHEMATICS | 2003年 / 47卷 / 03期
关键词：
D O I：
10.1215/ijm/1258138186
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish the local well-posedness for a new integrable equation. We prove that the equation has strong solutions that blow up in finite time and obtain the precise blow-up scenario for this equation. Moreover, we provide a framework of weak solutions for the study of soliton interaction.
引用
收藏
页码：649 / 666
页数：18
相关论文
共 50 条
  • [31] THE CAUCHY PROBLEM AND BLOW-UP PHENOMENA FOR A NEW INTEGRABLE TWO-COMPONENT PEAKON SYSTEM WITH CUBIC NONLINEARITIES
    Li, Xiuting
    Zhang, Lei
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (06) : 3301 - 3325
  • [32] A new two-component integrable system with peakon solutions
    Xia, Baoqiang
    Qiao, Zhijun
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2015, 471 (2175):
  • [33] Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation
    Lychagin, Valentin
    Yumaguzhin, Valeriy
    JOURNAL OF GEOMETRY AND PHYSICS, 2012, 62 (10) : 2099 - 2120
  • [34] Asymptotics behavior for the integrable nonlinear Schrodinger equation with quartic terms: Cauchy problem
    Huang, Lin
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2020, 27 (04) : 592 - 615
  • [35] THE CAUCHY PROBLEM FOR AN INTEGRABLE GENERALIZED CAMASSA-HOLM EQUATION WITH CUBIC NONLINEARITY
    Liu, Bin
    Zhang, Lei
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (01) : 267 - 296
  • [36] On the Cauchy problem for a combined mCH-Novikov integrable equation with linear dispersion
    Wan, Zhenyu
    Wang, Ying
    Zhu, Min
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 416 : 727 - 767
  • [37] On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity
    Fu, Ying
    Gui, Guilong
    Liu, Yue
    Qu, Changzheng
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (07) : 1905 - 1938
  • [38] Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions
    Jonatan Lenells
    Gerard Misiołek
    Feride Tiğlay
    Communications in Mathematical Physics, 2010, 299 : 129 - 161
  • [39] Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions
    Lenells, Jonatan
    Misiolek, Gerard
    Tiglay, Feride
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 299 (01) : 129 - 161
  • [40] An Isospectral Problem for Global Conservative Multi-Peakon Solutions of the Camassa–Holm Equation
    Jonathan Eckhardt
    Aleksey Kostenko
    Communications in Mathematical Physics, 2014, 329 : 893 - 918
12345