位移法浅水波方程的解及其特性

不同于传统流体力学，在Lagrange坐标下推导浅水波方程.若将水平位移作为基本变量，则推导出的浅水波数学模型可描述为固体力学的非线性大位移问题.运用不可压缩条件，通过变分原理推导出位移法浅水波方程，给出椭圆函数形式的行波解，并分析孤波解产生的条件.该基础研究建立了在分析结构力学中分析浅水波问题的理论基础，有利于进一步开展水动力学的研究.

Solutions and characteristics of shallow water equation based on displacement method

The shallow water wave equation is obtained in Lagrange coordinates, which is different from the traditional hydrodynamics. The horizontal displacement is defined as the basic variable, and the deduced mathematical model of shallow water wave just likes the nonlinear large displacement problem in solid mechanics. Under the incompressible condition, the variational principle for shallow water dynamic equation is given on the basis of the displacement method, and the corresponding elliptic traveling wave solutions are presented the conditions of obtaining solitary wave solutions are also discussed. As a basic research work, the present study establishes the theoretical foundation of analyzing the shallow water waves in analytical structural mechanics and is valuable for the further research in hydrodynamics.