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The stability of internal solitary waves

Published online by Cambridge University Press:  24 October 2008

D. P. Bennett ,
R. W. Brown ,
S. E. Stansfield ,
J. D. Stroughair  and
J. L. Bona
D. P. Bennett
Affiliation:
Physics Department, Case Western Reserve University, Cleveland, Ohio
R. W. Brown
Affiliation:
Physics Department, Case Western Reserve University, Cleveland, Ohio
S. E. Stansfield
Affiliation:
Physics Department, Case Western Reserve University, Cleveland, Ohio
J. D. Stroughair
Affiliation:
Physics Department, Case Western Reserve University, Cleveland, Ohio
J. L. Bona
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois
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Extract

A theory is developed relating to the stability of solitary-wave solutions of the so-called Benjamin-Ono equation. This equation was derived by Benjamin (5) as a model for the propagation of internal waves in an incompressible non-diffusive heterogeneous fluid for which the density is non-constant only within a layer whose thickness is much smaller than the total depth. In his article, Benjamin wrote in closed form the one-parameter family of solitary-wave solutions of his model equation whose stability will be the focus of attention presently.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 351 - 379
Copyright
Copyright © Cambridge Philosophical Society 1983

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