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

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dc.creatorParkes, E. John
dc.date2008-06-19
dc.date.accessioned2026-07-07T09:45:34Z
dc.date.available2026-07-07T09:45:34Z
dc.descriptionPeriodic 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.
dc.descriptionThis is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/0806.3155
dc.identifierhttp://arxiv.org/abs/0806.3155
dc.identifierSIGMA 4 (2008), 053, 17 pages
dc.identifierdoi:10.3842/SIGMA.2008.053
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163239
dc.subjectExactly Solvable and Integrable Systems
dc.subjectAnalysis of PDEs
dc.titlePeriodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation
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