李群法在水波方程中的应用

APPLICATIONS OF LIE GROUPS TO WAVE EQUATIONS

引入李群法对二维水波控制方程Laplace方程作群变换,利用同一解曲面的几何条件对其李代数进行降维,并借助于Mathematica计算软件,得到该控制方程的无限李群解,在考虑某边值问题的情况下,得出此问题的解析解。用李群法完成Laplace方程通解和某一特定边界条件特解的推导计算,证明了该方法的可行性。

Currently, there are some obstacles on the study of numerical methods of wave energy with nonlinear random waves. To solve this problem more accurately, this paper introduces a mathematical method, Lie Groups, as anexploration and a research. To the two-dimcnsinnal Laplace equation, it makes a Group transformation in surface of the Laplace equation. Using Side Condition to reduce the dimensions of the equation, and with the help of Mathematic software, it can obtain the infinite Lie Group solutions. After that, considering the boundary conditions, and doing further calculations, the analytic solutions can be obtained. This paper hase completed the derivations and the calculations, including the general solution of Laplace equation and the particular solution of a specified boundary condition, Using Lie Group. R have proved the feasibility of the method.