Title

Solitary-wave families of the Ostrovsky equation: An approach via reversible systems theory and normal forms

Authors

Authors

S. R. Choudhury

Comments

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Abbreviated Journal Title

Chaos Solitons Fractals

Keywords

SMALL PERIODIC-ORBITS; EMBEDDED SOLITONS; HOMOCLINIC ORBITS; VECTOR-FIELDS; RESONANCE; Mathematics, Interdisciplinary Applications; Physics, Multidisciplinary; Physics, Mathematical

Abstract

The Ostrovsky equation is an important canonical model for the unidirectional propagation of weakly nonlinear long surface and internal waves in a rotating, inviscid and incompressible fluid. Limited functional analytic results exist for the occurrence of one family of solitary-wave solutions of this equation, as well as their approach to the well-known solitons of the famous Korteweg-de Vries equation in the limit as the rotation becomes vanishingly small. Since solitary-wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves and its reduction to the KdV limit, we find a second family of multi-humped (or N-pulse) solutions, as well as a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. The second and third families of solutions occur in regions of parameter space distinct from the known solitary-wave solutions and are thus entirely new. Directions for future work are also mentioned. (c) 2006 Elsevier Ltd. All rights reserved.

Journal Title

Chaos Solitons & Fractals

Volume

33

Issue/Number

5

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

1468

Last Page

1479

WOS Identifier

WOS:000246546500005

ISSN

0960-0779

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