Title

Solitary wave families of a generalized microstructure PDE

Authors

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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