Hamilton体系下的二维非线性浅水波

Hamiltonian structure and two dimensional nonlinear waves in shallow water

从Ｈａｍｉｌｔｏｎ体系出发推导出二维浅水波问题的非线性动力方程组。通过讨论给出该问题的一阶近似、二阶近似等。具体求解得到该问题的行波解，此解可由椭圆积分所表示。结果表明波形不仅与波速有关，而且与水深等有关。

Based on Hamiltonian structure,nonlinear dynamic equations of two dimensionalshallow water-waves are studied. Hamiltonian first order , second order approximations and so onare obtained. The solutions of the travelling waves can be expressed by elliptical integrals. Theresults show that the forms of waves depend not only on wave speed but also on water depth.