Solitary wave families of a generalized microstructure PDE

    Authors

    J. A. Leto;S. R. Choudhury

    Abbreviated Journal Title

    Commun. Nonlinear Sci. Numer. Simul.

    Keywords

    Generalized microstructure PDE; Solitary wave families; Reversible; systems; Homoclinic orbits; SMALL PERIODIC-ORBITS; REVERSIBLE-SYSTEMS; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical

    Abstract

    Wave propagation in a generalized microstructure PDE, tinder the Mindlin relations, is considered. Limited analytic results exist for the occurrence of one family of solitary wave solutions of these equations. Since solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions here (via normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves, we find 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 new family 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) 2008 Elsevier B.V. All rights reserved.

    Journal Title

    Communications in Nonlinear Science and Numerical Simulation

    Volume

    14

    Issue/Number

    5

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    1999

    Last Page

    2005

    WOS Identifier

    WOS:000264296000024

    ISSN

    1007-5704

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