Title

Solitary-Wave Families Of The Ostrovsky Equation: An Approach Via Reversible Systems Theory And Normal Forms

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 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 are also mentioned. © 2006 Elsevier Ltd. All rights reserved.

Publication Date

8-1-2007

Publication Title

Chaos, Solitons and Fractals

Volume

33

Issue

5

Number of Pages

1468-1479

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.chaos.2006.02.010

Socpus ID

33947112329 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33947112329

This document is currently not available here.

Share

COinS