Title

Solitary Wave Families Of Nlpdes Via Reversible Systems Theory

Keywords

Reversible systems theory; Solitary wave families

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. 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 multihumped (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, including on other NLPDEs, are also mentioned. © 2009 IMACS.

Publication Date

9-1-2009

Publication Title

Mathematics and Computers in Simulation

Volume

80

Issue

1

Number of Pages

37-45

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.matcom.2009.06.029

Socpus ID

70349166310 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/70349166310

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