On a nonlinear problem of the breaking water waves

M. Kirane; B. T. Torebek

doi:10.14529/mmp190203

On a nonlinear problem of the breaking water waves

M. Kirane, B. T. Torebek

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	British English
Pages (from-to)	37-46
Number of pages	10
Journal	Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software
Volume	12
Issue number	2
DOIs	https://doi.org/10.14529/mmp190203
State	Published - 2019

Keywords

Blow-up of solution
Breaking waves
Initial-boundary problems
Korteweg-de Vries-Benjamin-Bona-Mahony equation

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10.14529/mmp190203

Cite this

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title = "On a nonlinear problem of the breaking water waves",

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 = "Blow-up of solution, Breaking waves, Initial-boundary problems, Korteweg-de Vries-Benjamin-Bona-Mahony equation",

author = "M. Kirane and Torebek, {B. T.}",

note = "Funding Information: Acknowledgements. The second named author is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant No. AP05131044). Publisher Copyright: {\textcopyright} 2019 South Ural State University. All rights reserved.",

year = "2019",

doi = "10.14529/mmp190203",

language = "British English",

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AU - Kirane, M.

AU - Torebek, B. T.

N1 - Funding Information: Acknowledgements. The second named author is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant No. AP05131044). Publisher Copyright: © 2019 South Ural State University. All rights reserved.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Blow-up of solution

KW - Breaking waves

KW - Initial-boundary problems

KW - Korteweg-de Vries-Benjamin-Bona-Mahony equation

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VL - 12

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JO - Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software

JF - Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software

IS - 2

ER -

On a nonlinear problem of the breaking water waves

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