On a class of Boussinesq equations for shallow water waves

Authors:
Prabir Daripa;Ranjan K. Dash
Affiliations:
Department of Mathematics, Texas A&M University, College Station, TX;Department of Bioengineering, University of Washington, Seattle, WA
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Year:
2003

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Abstract

The Euler's equations describing the dynamics of capillary-gravity water waves in two-dimensions are considered in the limits of small-amplitude and long-wavelength under appropriate boundary conditions. Using a double-series perturbation analysis, a general Boussinesq type of equation is derived involving the small-amplitude and long-wavelength parameters. A recently introduced sixth-order Boussinesq equation by Daripa and Hua [Appl. Math. Comput. 101 (1999), 159- 207] is recovered from this equation in the 1/3 Bond number limit (from below) when the above parameters bear a certain relationship as they approach zero.