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Mathematical Modelling
On a nonlinear problem of the breaking water waves
M. Kiranea, B. T. Torebekbc a Université de La Rochelle, La Rochelle, France
b Al-Farabi Kazakh National University, Almaty, Kazakhstan
c Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Abstract:
The paper is devoted to the initial boundary value problem for the Korteweg-de Vries–Benjamin–Bona–Mahony equation in a finite domain. This particular problem arises from the phenomenon of long wave with small amplitude in fluid. For certain initial-boundary problems for the Korteweg-de Vries–Benjamin–Bona–Mahony equation, we obtain the conditions of blowing-up of global and travelling wave solutions in finite time. The proof of the results is based on the nonlinear capacity method. In closing, we provide the exact and numerical examples.
Keywords:
breaking waves, Korteweg-de Vries–Benjamin–Bona–Mahony equation, blow-up of solution, initial-boundary problems.
Received: 09.10.2018
Citation:
M. Kirane, B. T. Torebek, “On a nonlinear problem of the breaking water waves”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:2 (2019), 37–46
Linking options:
https://www.mathnet.ru/eng/vyuru486 https://www.mathnet.ru/eng/vyuru/v12/i2/p37
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Abstract page: | 223 | Full-text PDF : | 132 | References: | 88 |
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