位移法浅水孤立波

浅水波的速度分布与z无关，表明位移也与z无关，相当于杆件的刚性横截面假定．采用物质坐标，用水平位移作为基本未知量，成为固体力学的非线性大位移问题．于是，分析力学的变分原理都可运用了，正则变换、近似解的保辛积分等有效手段可使数值求解方便很多,对干孤立波。则其方程已不再是KdV方程。但仍然得到了孤立波的解．从而是一种值得探讨的方法．

Shallow water solitary waves based on displacement method

The velocity distribution of the shallow water wave is independent of z, which indicates that the displacement is independent of z also. This is just equivalent to the supposition of the rigid cross-section in bars. Under the physical coordinate, the horizontal displacement is taken as an unknown quantity, and a nonlinear problem with big displacement of solid mechanics is introduced. Hence the variational principle of the analytic mechanics can be applied. And the numerical results can be more conveniently got by using efficient means, such as canonical transformation, and symplectic conservative integration of the simplified solution. The shallow water solitary wave equation, not KdV equation, is educed by the displacement method, and the solutions of the solitary waves are still presented. The exploratory investigation of this method is a worthwhile work.