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__On some systems for internal wave propagation__

A. Durán and D. Mitsotakis

**Abstract**

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.

**Bibliography**

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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.

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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.