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

    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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