SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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On some systems for internal wave propagation

A. Durán and D. Mitsotakis

We consider a system of Benjamin-Ono type for the propagation of internal waves over a horizontal bottom and a rigid lid. First we study the existence of solitary waves by numerical means while in a special case we present analytical formulas of solitary waves that decay with a polynomial order. An efficient numerical method for the integration of the specific system will be introduced and checked with several experiments, including solitary-wave interactions and stability. Some comparisons with the classical Benjamin-Ono equation will also be made.

[1] J.L. Bona, D. Lannes and J.C. Saut, Asymptotic models for internal waves, J. Math. Pures Appl., 89 (2008), pp. 538-566.
[2] V. Duchene, Asymptotic shallow water models for internal waves in a two-fluid system with a free surface, SIAM J. Math. Anal., 42 (2010), pp. 2229-2260.
[3] P. Guyenne, D. Lannes and J.C. Saut, Well-posedness of the Cauchy problem for models of large amplitude internal waves. Nonlinearity, 23 (2010), pp. 237-275.

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