scholarly journals Ermakov Equation and Camssa-Holm Waves

2016 ◽  
Vol 34 (1-2) ◽  
pp. 47-51
Author(s):  
Haret C. Rosu ◽  
Stefan C. Mancas
Keyword(s):  
Shallow Water ◽  
Spectral Problem ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Important Ingredient ◽  
Interesting Issue ◽  
Holm Equation

Since the works of [1] and [2], it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.

The string density problem and the Camassa–Holm equation

2007 ◽  
Vol 365 (1858) ◽  
pp. 2299-2312 ◽  
Author(s):  
Richard Beals ◽  
David H Sattinger ◽  
Jacek Szmigielski
Keyword(s):  
Inverse Problem ◽  
Special Reference ◽  
Shallow Water ◽  
Spectral Problem ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Numerical Examples ◽  
Holm Equation ◽  
Density Problem

Recently, the string density problem, considered in the pioneering work of M. G. Krein, has arisen naturally in connection with the Camassa–Holm equation for shallow water waves. In this paper we review the forward and inverse string density problems, with some numerical examples, and relate it to the Camassa–Holm equation, with special reference to multi-peakon/anti-peakon solutions. Under stronger assumptions, the Camassa–Holm spectral problem and the string density problem can be transformed to the Schrödinger spectral problem and its inverse problem. Recent results exploiting this transformation are reviewed briefly.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach

scholarly journals Diverse novel analytical and semi-analytical wave solutions of the generalized (2+1)-dimensional shallow water waves model

AIP Advances ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 015223
Author(s):  
Yuming Chu ◽  
Mostafa M. A. Khater ◽  
Y. S. Hamed
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Wave Solutions

scholarly journals Active-subspace analysis of exceedance probability for shallow-water waves

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Kenan Šehić ◽  
Henrik Bredmose ◽  
John D. Sørensen ◽  
Mirza Karamehmedović
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Exceedance Probability ◽  
Subspace Analysis ◽  
Shallow Water Waves ◽  
Active Subspace

scholarly journals Shallow water waves in a rotating rectangular basin

2000 ◽  
Vol 24 (10) ◽  
pp. 649-661 ◽  
Author(s):  
Mohamed Atef Helal
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Equations Of Motion ◽  
System Of Nonlinear Equations ◽  
System Of Equations ◽  
Order Of Approximation ◽  
Shallow Water Waves ◽  
Nonlinear System Of Equations ◽  
Rectangular Basin ◽  
Shallow Water Approximation

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating rectangular basin. The equations of motion of such a problem with its boundary conditions are reduced to a system of nonlinear equations, which is to be solved by applying the shallow water approximation theory. Each unknown of the problem is expanded asymptotically in terms of the small parameterϵwhich generally depends on some intrinsic quantities of the problem of study. For each order of approximation, the nonlinear system of equations is presented successively. It is worthy to note that such a study has useful applications in the oceanography.

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