Abstract
A general theory for determining Hamiltonian model equations from noncanonical perturbation expansions of Hamiltonian systems is applied to the Boussinesq expansion for long, small amplitude waves in shallow water, leading to the Korteweg-de-Vries equation.New Hamiltonian model equations, including a natural “Hamiltonian version” of the KdV equation, are proposed. The method also provides a direct explanation of the complete integrability (soliton property) of the KdV equation. Depth dependence in both the Hamiltonian models and the second order standard perturbation models is discussed as a possible mechanism for wave breaking.
Research supported in part by National Science Foundation Grant NSF MCS 81-00786.
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© 1984 Springer-Verlag
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Olver, P.J. (1984). Hamiltonian and non-Hamiltonian models for water waves. In: Ciarlet, P.G., Roseau, M. (eds) Trends and Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12916-2_62
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DOI: https://doi.org/10.1007/3-540-12916-2_62
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