Models for internal waves in deep water

Jerry L. Bona; Henrik Kalisch

doi:10.3934/dcds.2000.6.1

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2000, Volume 6, Issue 1: 1-20. Doi: 10.3934/dcds.2000.6.1

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Models for internal waves in deep water

Jerry L. Bona^1, and
Henrik Kalisch^2,

1.
Department of Math. and Texas Institute for Computational & Applied Math., University of Texas, Austin, TX 78712
2.
Department of Mathematics, University of Texas, Austin, TX 78712

Received: November 1999

Published: January 2000

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Abstract

We study properties of solitary-wave solutions of three evolution equations arising in the modeling of internal waves. Our experiments indicate that broad classes of initial data resolve into solitary waves, but also suggest that solitary waves do not interact exactly, thus suggesting two of these equations are not integrable. In the course of our numerical simulations, interesting meta-stable quasi-periodic structures have also come to light.

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Mathematics Subject Classification: 35S10, 35Q53, 37K10, 45K05, 47G20, 65M70, 76B25, 76B55.

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