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January  2000, 6(1): 1-20. doi: 10.3934/dcds.2000.6.1

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, United States
2. 

Department of Mathematics, University of Texas, Austin, TX 78712, United States

Received  November 1999 Published  December 1999

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.
Keywords: Nonlinear Waves, Solitons, Integro­differential Equations, Solitary­Wave Interaction., Spectral Methods.
Mathematics Subject Classification: 35S10, 35Q53, 37K10, 45K05, 47G20, 65M70, 76B25, 76B55. .
Citation: Jerry L. Bona, Henrik Kalisch. Models for internal waves in deep water. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 1-20. doi: 10.3934/dcds.2000.6.1
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