Wave Breaking for the Modified Two-Component Camassa-Holm System

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

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Wave Breaking Phenomenon for DGH Equation with Strong Dissipation

Abstract and Applied Analysis ◽

10.1155/2014/169423 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Zhengguang Guo ◽

Min Zhao

Keyword(s):

Finite Time ◽

Wave Breaking ◽

Blow Up ◽

Sufficient Conditions ◽

Strong Solutions ◽

Dissipative Term

The present work is mainly concerned with the Dullin-Gottwald-Holm (DGH) equation with strong dissipative term. We establish some sufficient conditions to guarantee finite time blow-up of strong solutions.

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On the wave-breaking phenomena for the two-component Dullin-Gottwald-Holm system

Journal of the London Mathematical Society ◽

10.1112/jlms/jds035 ◽

2012 ◽

Vol 86 (3) ◽

pp. 810-834 ◽

Cited By ~ 24

Author(s):

Fei Guo ◽

Hongjun Gao ◽

Yue Liu

Keyword(s):

Wave Breaking ◽

Two Component

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Wave breaking for a generalized weakly dissipative two-component Camassa–Holm system

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.10.063 ◽

2013 ◽

Vol 400 (2) ◽

pp. 406-417 ◽

Cited By ~ 5

Author(s):

Wenxia Chen ◽

Lixin Tian ◽

Xiaoyan Deng ◽

Jianmei Zhang

Keyword(s):

Wave Breaking ◽

Two Component

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On the wave-breaking phenomena for the periodic two-component Dullin–Gottwald–Holm system

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.02.058 ◽

2012 ◽

Vol 391 (2) ◽

pp. 415-428 ◽

Cited By ~ 17

Author(s):

Min Zhu ◽

Junxiang Xu

Keyword(s):

Wave Breaking ◽

Two Component

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Stability of blow-up solution for the two component Camassa–Holm equations

Asymptotic Analysis ◽

10.3233/asy-191590 ◽

2020 ◽

Vol 120 (3-4) ◽

pp. 319-336

Author(s):

Xintao Li ◽

Shoujun Huang ◽

Weiping Yan

Keyword(s):

Shallow Water ◽

Wave Breaking ◽

Water Regime ◽

Blow Up ◽

Dynamical Behavior ◽

Water Dynamics ◽

Two Component ◽

Breaking Mechanism ◽

Self Similar ◽

Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

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