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Stability of Forced Steady Solitary Waves

Camassa, R. and Wu, T. Yao-tsu (1991) Stability of Forced Steady Solitary Waves. Philosophical Transactions: Physical Sciences and Engineering, 337 (1648). pp. 429-466. ISSN 0962-8428. https://resolver.caltech.edu/CaltechAUTHORS:20141217-132715581

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Abstract

This paper explores the basic mechanism underlying the remarkable phenomenon that a forcing excitation stationary in character and sustained at near resonance in a shallow channel of uniform water depth generates a non-stationary response in the form of a sequential upstream emission of solitary waves. Adopting the forced Korteweg-de Vries (fKdV) model and using two of its steady forced solitary wave solutions as primary flows, the stability of these two transcritical steady motions is investigated, and their bifurcation diagrams relating these solutions to other stationary solutions determined, with the forcing held fixed. The corresponding forcing functions are characterized by a velocity parameter for one, and an amplitude parameter for the other of the steadily moving excitations.


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http://www.jstor.org/stable/53977JSTORArticle
Additional Information:© 1991 The Royal Society. Received 2 October 1990; revised 19 April 1991; accepted 31 May 1991. We take pleasure in expressing our deep gratitude to Sir James Lighthill for extremely valuable discussions, especially those concerning the case when the rate of growth of the unstable stationary motions is weak. We are indebted to George Yates for useful discussions and for his invaluable assistance in the numerical computations. This work was jointly sponsored by ONR Contract N00014-82-K-0443, NSF Grant MSM-8706045 and their successors N00014-89-J1971 and NSF 4 DMS-890 1440, the last being cosponsored by the Applied Mathematics, Computational Mathematics and Fluid Dynamics/Hydraulics Programs. One of us (R.C.) also acknowledges support by DOE Contract W-7045-ENG-36 and AFOSRISSA 900024. The numerical calculation were performed on the CRAY X-MP/48 at San Diego Supercomputer Center and at the National Center for supercomputing Applications (operated by the National Science Foundation).
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-82-K-0443
NSFMSM-8706045
Office of Naval Research (ONR)N00014-89-J1971
NSFDMS-890 1440
Department of Energy (DOE)W-7045-ENG-36
Air Force Office of Scientific Research (AFOSR)AFOSRISSA 900024
Issue or Number:1648
Record Number:CaltechAUTHORS:20141217-132715581
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141217-132715581
Official Citation:Stability of Forced Steady Solitary Waves R. Camassa and T. Yao-Tsu Wu Philosophical Transactions: Physical Sciences and Engineering Vol. 337, No. 1648 (Dec. 15, 1991) , pp. 429-466 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/53977
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52967
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Dec 2014 22:43
Last Modified:03 Oct 2019 07:46

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