Models for internal waves in deep water

Pages: 1 - 20, Volume 6, Issue 1, January 2000

doi:10.3934/dcds.2000.6.1       Abstract        Full Text (374.6K)       Related Articles

Jerry L. Bona - Department of Math. and Texas Institute for Computational & Applied Math., University of Texas, Austin, TX 78712, United States (email)
Henrik Kalisch - Department of Mathematics, University of Texas, Austin, TX 78712, United States (email)

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.

Keywords:  Nonlinear Waves, Solitons, Integro­differential Equations, Spectral Methods, Solitary­Wave Interaction.
Mathematics Subject Classification:  35S10, 35Q53, 37K10, 45K05, 47G20, 65M70, 76B25, 76B55.

Received: November 1999;      Published: December 1999.