Solitary Waves, Shock Waves and Singular Solitons of Gardner's Equation for Shallow Water Dynamics

2014 ◽  
Vol 45 (6) ◽  
pp. 1135
Author(s):  
A.K. Daoui ◽  
H. Triki ◽  
M. Mirzazadeh ◽  
A. Biswas
Keyword(s):  
Shock Waves ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Dynamics ◽  
Shallow Water Dynamics

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.

A simple justification of the singular limit for equatorial shallow-water dynamics

2009 ◽  
Vol 62 (3) ◽  
pp. 322-333 ◽  
Author(s):  
Alexandre Dutrifoy ◽  
Steven Schochet ◽  
Andrew J. Majda
Keyword(s):  
Shallow Water ◽  
Singular Limit ◽  
Water Dynamics ◽  
Shallow Water Dynamics

scholarly journals Shallow water dynamics on linear shear flows and plane beaches

2017 ◽  
Vol 29 (7) ◽  
pp. 073602 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Water Dynamics ◽  
Linear Shear ◽  
Shallow Water Dynamics
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