Open Access
June 2005 Approximate Model Equations for Water Waves
Razan Fetecau, Doron Levy
Commun. Math. Sci. 3(2): 159-170 (June 2005).


We present two new model equations for the unidirectional propagation of long waves in dispersive media for the specific purpose of modeling water waves. The derivation of the new equations uses a Pade(2,2) approximation of the phase velocity that arises in the linear water wave theory. Unlike the Korteweg-deVries (KdV) equation and similarly to the Benjamin-Bona-Mahony (BBM) equation, our models have a bounded dispersion relation. At the same time, the equations we propose provide the best approximation of the phase velocity for small wave numbers that can be obtained with third-order equations. We note that the new model equations can be transformed into previously studied models, such as the BBM and the Burgers-Poisson equations. It is therefore straightforward to establish the existence and uniqueness of solutions to the new equations. We also show that the distance between the solutions of one of the new equations, the KdV equation, and the BBM equation, is of the small order that is formally neglected by all models.


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Razan Fetecau. Doron Levy. "Approximate Model Equations for Water Waves." Commun. Math. Sci. 3 (2) 159 - 170, June 2005.


Published: June 2005
First available in Project Euclid: 14 June 2005

zbMATH: 1101.35065
MathSciNet: MR2164195

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 2 • June 2005
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