Abstract
In the first part of this paper the Hamiltonian theory of water waves is used to obtain some equations in local coordinates. These equations are approximations of the Boussinesq type. They are stable with respect to short wave perturbations, e.g. rounding off errors in digital computing. In the second part the relation of Boussinesq equations to Korteweg-de Vries and Benjamin-Bona-Mahony equations is investigated.
Similar content being viewed by others
References
Broer, L. J. F., Appl. Sci. Res. 29 (1974) 430.
Broer, L. J. F., Physica, 79H (1975) 583.
Dingemans, M. W., Report R 729-II, Delft Hydraulics Laboratory, 1973.
Benjamin, T. B., Bona, J. L. and J. J. Mahony, Phil. Trans. Roy. Soc. London, 272, A 1220 (1972) 47.
Broer, L. J. F. and L. A. Peletier, Appl. Sci. Res. 21 (1969) 138.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Broer, L.J.F. Approximate equations for long water waves. Appl. sci. Res. 31, 377–395 (1975). https://doi.org/10.1007/BF00418048
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00418048