论文标题
对称，保护法，不变解决方案和差异方案的差异方案
Symmetries, conservation laws, invariant solutions and difference schemes of the one-dimensional Green-Naghdi equations
论文作者
论文摘要
该论文专门介绍了一维绿色 - 纳格迪方程的Lie组特性，这些方程描述了流体流动在不平坦的底部地形上的行为。底部的地形以两种方式合并到绿色 - 纳格迪方程中：以经典的绿色 - 纳格迪形式和相同顺序的近似形式。该研究是在拉格朗日坐标中进行的，该坐标使一个人可以找到分析方程的拉格朗日。介绍了两种绿色纳格迪方程相对于底部地形的完整小组分类。采用Noether定理，获得的Lagrangians和群体分类，获得具有不均底形图不均匀的一维绿色NAGHDI方程的保护定律。构建了保留原始方程和保护定律的对称性的差异方案。给出了开发方案的分析。这些方案以数值测试的示例以精确的行进波解决方案进行了测试。
The paper is devoted to the Lie group properties of the one-dimensional Green-Naghdi equations describing the behavior of fluid flow over uneven bottom topography. The bottom topography is incorporated into the Green-Naghdi equations in two ways: in the classical Green-Naghdi form and in the approximated form of the same order. The study is performed in Lagrangian coordinates which allows one to find Lagrangians for the analyzed equations. Complete group classification of both cases of the Green-Naghdi equations with respect to the bottom topography is presented. Applying Noether's theorem, the obtained Lagrangians and the group classification, conservation laws of the one-dimensional Green-Naghdi equations with uneven bottom topography are obtained. Difference schemes which preserve the symmetries of the original equations and the conservation laws are constructed. Analysis of the developed schemes is given. The schemes are tested numerically on the example of an exact traveling-wave solution.
