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Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation

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dc.contributor.author Parkes, E.J.
dc.date.accessioned 2019-02-19T13:09:06Z
dc.date.available 2019-02-19T13:09:06Z
dc.date.issued 2008
dc.identifier.citation Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation / E.J. Parkes // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2000 Mathematics Subject Classification: 35Q58; 35Q53: 35C05
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/149028
dc.description.abstract Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves. uk_UA
dc.description.sponsorship This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The author thanks the referees for some perceptive comments and for recommending some additional references. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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