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Research progress on theories and applications of Hamiltonian system in nonlinear water waves 

Zhang Baoshan, Lu Dongqiang, Dai Shiqiang, Cheng Youliang
(Shanghai Institute of Applied Mathematics & Mechanics, Shanghai University, Shanghai, China, 200072)

Abstract: This paper is a summary of the applications of symplectic theories algorithms to Hamiltonian mechanics and the research progress Hamiltonian formulation for nonlinear water waves. The advantages and limitations of Hamiltonian variational principle and approaches for nonlinear water waves are discussed. In addition, it includes also discussions on the Hamiltonian formalism, symmetry and conservation laws of KdV equation and BBM equation and comments on the problems concerned.
Keywords: Hamiltonian principle, symplectic geometry, nonlinear water waves, Hamiltonian systems, symmetry and conservation laws.

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1Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System

2Free-surface waves and far wakes generated by a floating body in a viscous fluid

3Poisson ̖xµğoFSLie

4INTERACTION OF VISCOUS WAKES WITH A FREE SURFACE

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