李群方法求解Regularized-Long-Wave方程及对其解的参数分析

Lie symmetry method of solving Regularized-Long-Wave equation and parameter analysis of its solution

运用李对称群方法,通过构造群不变量作为函数变换的基础,使偏微分方程减少一个自变量得到化简,约化为常微分方程并求其解析解。应用此法求出Regularized-Long-Wave方程的全部李点对称,并用特殊的对称将其约化为相应的常微分方程,对其中一种常微分方程进行求解。利用海洋水文资料对求出的解进行内波参数分析,发现无论对于下降型内波还是上升型内波,密度跃层差异△ρ/ρ越大,方程参数线性速度C_0越大,内波纵向位移越小。对于下降型内波来说,密度跃层深度h_1越大,线性速度C_0越大,则方程一阶非线性项系数α越大,弥散项系数β也越大,从而内波纵向位移越大;对于上升型内波而言,密度跃层深度h_1越小,线性速度C_0越大,则α越小,β越大,从而内波纵向位移越大。

All symmetries of the Regularized-Long-Wave equation are worked out by method of infinitesimal generator of Lie group of transformation. One of the ordinary differential equations are derived by using the particular symmetry and then solve its equation. The solution is analyzed by means of oceanographic hydrological data, finding that the greater the difference of pycnocline △ρ/ρ, the linear velocity parameter Co would mean greater,thus me smaucr longitudinal both for rising and dropping type internal waves. For dropping type internal waves, the bigger the depth of pycnocline hi, the linear velocity parameter Co would mean greater, and so does coefficient of the first order nonlinear term a and coefficient of the dispersion term/3, thus the bigger longitudinal displacement of internal waves. For rising type internal waves ,the smaller the depth of pycnocline h~, the parameter Co would mean greater, a would be smaller,/3 would mean greater, thus the bigger longitudinal displacement of internal waves.