Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

Dmitry G. Arkhipov; Georgy A. Khabakhpashev; Vladimir E. Zakharov

doi:10.1016/j.physleta.2015.03.010

Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

Dmitry G. Arkhipov
, Georgy A. Khabakhpashev
, Vladimir E. Zakharov

Mathematics

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

6 Scopus citations

Abstract

A single nonlinear partial differential equation of the wave type for an axisymmetric case is obtained by the introduction of special auxiliary function. In contrast to cylindrical Korteweg-de Vries equation, new equation describes centrifugal and centripetal waves not only far from the center, but in its vicinity as well. With the use of this equation a number of specific problems on the evolution of the free surface disturbances are numerically solved for the cases of a horizontal bottom and a drowned concave. The research also demonstrates the difference between the results of calculations on the base of the complete equation and on the basis of the linearized equation.

Original language	English (US)
Pages (from-to)	1414-1417
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	379
Issue number	22-23
DOIs	https://doi.org/10.1016/j.physleta.2015.03.010
State	Published - Jul 17 2015

Keywords

Axisymmetric disturbance
Centrifugal wave
Centripetal wave
Interaction of disturbances
Nonlinear wave
Transformation of disturbance

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.physleta.2015.03.010

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title = "Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation",

abstract = "A single nonlinear partial differential equation of the wave type for an axisymmetric case is obtained by the introduction of special auxiliary function. In contrast to cylindrical Korteweg-de Vries equation, new equation describes centrifugal and centripetal waves not only far from the center, but in its vicinity as well. With the use of this equation a number of specific problems on the evolution of the free surface disturbances are numerically solved for the cases of a horizontal bottom and a drowned concave. The research also demonstrates the difference between the results of calculations on the base of the complete equation and on the basis of the linearized equation.",

keywords = "Axisymmetric disturbance, Centrifugal wave, Centripetal wave, Interaction of disturbances, Nonlinear wave, Transformation of disturbance",

author = "Arkhipov, \{Dmitry G.\} and Khabakhpashev, \{Georgy A.\} and Zakharov, \{Vladimir E.\}",

note = "Funding Information: We are grateful to E.A. Kuznetsov, L.A. Ostrovsky, E.N. Pelinovsky, and Yu.A. Stepanyants for valuable discussions of this investigation, and to the reviewer for his comments that allowed significantly improving this article. The study was financed by the Russian Science Foundation (grant No. 14-22-00174 ). Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.All rights reserved.",

year = "2015",

month = jul,

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doi = "10.1016/j.physleta.2015.03.010",

language = "English (US)",

volume = "379",

pages = "1414--1417",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

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T1 - Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

AU - Arkhipov, Dmitry G.

AU - Khabakhpashev, Georgy A.

AU - Zakharov, Vladimir E.

N1 - Funding Information: We are grateful to E.A. Kuznetsov, L.A. Ostrovsky, E.N. Pelinovsky, and Yu.A. Stepanyants for valuable discussions of this investigation, and to the reviewer for his comments that allowed significantly improving this article. The study was financed by the Russian Science Foundation (grant No. 14-22-00174 ). Publisher Copyright: © 2015 Elsevier B.V.All rights reserved.

PY - 2015/7/17

Y1 - 2015/7/17

N2 - A single nonlinear partial differential equation of the wave type for an axisymmetric case is obtained by the introduction of special auxiliary function. In contrast to cylindrical Korteweg-de Vries equation, new equation describes centrifugal and centripetal waves not only far from the center, but in its vicinity as well. With the use of this equation a number of specific problems on the evolution of the free surface disturbances are numerically solved for the cases of a horizontal bottom and a drowned concave. The research also demonstrates the difference between the results of calculations on the base of the complete equation and on the basis of the linearized equation.

AB - A single nonlinear partial differential equation of the wave type for an axisymmetric case is obtained by the introduction of special auxiliary function. In contrast to cylindrical Korteweg-de Vries equation, new equation describes centrifugal and centripetal waves not only far from the center, but in its vicinity as well. With the use of this equation a number of specific problems on the evolution of the free surface disturbances are numerically solved for the cases of a horizontal bottom and a drowned concave. The research also demonstrates the difference between the results of calculations on the base of the complete equation and on the basis of the linearized equation.

KW - Axisymmetric disturbance

KW - Centrifugal wave

KW - Centripetal wave

KW - Interaction of disturbances

KW - Nonlinear wave

KW - Transformation of disturbance

UR - https://www.scopus.com/pages/publications/84940001479

UR - https://www.scopus.com/pages/publications/84940001479#tab=citedBy

U2 - 10.1016/j.physleta.2015.03.010

DO - 10.1016/j.physleta.2015.03.010

M3 - Article

SN - 0375-9601

VL - 379

SP - 1414

EP - 1417

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 22-23

ER -

Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

Abstract

Keywords

ASJC Scopus subject areas

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