Erratum to “On the Cauchy problem for a model equation for shallow water waves of moderate amplitude” [Nonlinear Anal. RWA 14 (5) (2013) 2022–2026]

2020 ◽  
Vol 53 ◽  
pp. 103073
Author(s):  
N. Duruk Mutlubaş
Keyword(s):  
Cauchy Problem ◽  
Shallow Water ◽  
Water Waves ◽  
Model Equation ◽  
Shallow Water Waves ◽  
Nonlinear Anal ◽  
The Cauchy Problem

scholarly journals Camassa-Holm equation on shallow water wave equation

2017 ◽  
Vol 5 (12) ◽  
pp. 7758-7764
Author(s):  
Sh. Hajrulla, L. Bezati, F. Hoxha
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Weak Solution ◽  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Kdv Equation ◽  
Shallow Water Wave ◽  
Holm Equation ◽  
The Cauchy Problem

In this paper we can consider the problem of week solutions for the general shallow water wave equation. In the first part of this paper, we deal to the well-known Kdv equation. We obtain the Camassa-Holm equation in particular. Both of them describe unidirectional shallow water waves equation. Moreover, all these equations have a bi-Hamiltonian structure, they are completely integrable, they have infinitely many conserved quantities. From a mathematical point of view the Camassa-Holm equation is well studied. In the second part of this paper, we obtain a global weak solution as a limit of approximation under the assumption  Some concepts related to high dimensional spaces are considered. Then the Cauchy problem is considered. It has an admissible weak solution  to the Cauchy problem for  Existence, uniqueness, and basic energy estimate on this approximate solution sequence are given in some lemmas. Finally, the main theorem and the proof is given

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
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