scholarly journals Liouville theorems for periodic two-component shallow water systems

2018 ◽  
Vol 38 (6) ◽  
pp. 3085-3097
Author(s):  
Qiaoyi Hu ◽  
◽  
Zhixin Wu ◽  
Yumei Sun ◽  
◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Systems ◽  
Liouville Theorems ◽  
Two Component

Modeling ship-induced waves in shallow water systems: The Venice experiment

2018 ◽  
Vol 155 ◽  
pp. 227-239 ◽  
Author(s):  
D. Bellafiore ◽  
L. Zaggia ◽  
R. Broglia ◽  
C. Ferrarin ◽  
F. Barbariol ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Systems

Non-uniform dependence on initial data for the two-component fractional shallow water wave system

2020 ◽  
Vol 192 ◽  
pp. 111714
Author(s):  
Shouming Zhou ◽  
Shihang Pan ◽  
Chunlai Mu ◽  
Honglin Luo
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Water Wave ◽  
Wave System ◽  
Shallow Water Wave ◽  
Two Component

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

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.

Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

2020 ◽  
Vol 30 (03) ◽  
pp. 2050036 ◽  
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Two Component ◽  
Wave Models

For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

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