Hamiltonian and Non - Hamiltonian Modeis Pcs Water Waves

A. general theory for determining Hamiltonian model equations from noncanonical perturbation expansions of Hamiltonian systems is applied to the Boussinesq expan sion fcr long, small amplitude waves in shallow water, leading to the Korteweg-deVries equation. New Hamiltonian model equations, including a natural "Hamiltonian ver-cn» of the KdV equation, are proposed. The method also provides a direct expiation of the complete integrability (soliton property) of the KdV equation. Depti dependence in both the Hamiltonian models and the second order standard perturbation models is discussed as a possible mechanism for vave breaking.