Solitary wave families of NLPDES via reversible systems theory

    Authors

    S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Math. Comput. Simul.

    Keywords

    Solitary wave families; Reversible systems theory; SMALL PERIODIC-ORBITS; OSTROVSKY EQUATION; HOMOCLINIC ORBITS; VECTOR-FIELDS; SOLITONS; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied

    Abstract

    The Ostrovsky equation is an important canonical model for the undirectional propagation of weakly nonlinear long surface and internal waves in a rotating, mviscid and incompressible fluid. Since solitary wave solutions often play a central role in the long-time evolution of an inital disturbance. we consider such solutions here (via the normal form approach) within the framework of reversible system theory. Resides confirming the existence of the known family of solitary waves and its reduction to the Kdv limit. w we find a second family of multihumped (or N-pulse) solutions, as well as a contimum 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 solutions. 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, including on other NLPDEs, are also mentioned. (C) 2009 IMACS Published by Elsevier B.V. All rights reserved.

    Journal Title

    Mathematics and Computers in Simulation

    Volume

    80

    Issue/Number

    1

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    37

    Last Page

    45

    WOS Identifier

    WOS:000271103800006

    ISSN

    0378-4754

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