CAJ | 학술논문

李群理论的对称分析常用于简化微分方程的求解，并且被有效地用于解决非线性问题。本文利用经典的李群分析方法讨论一类在工程和物理领域有着广泛应用的二维形式板振动的四阶偏微分方程的最优对称和精确解。首先，利用无穷小生成元方法求得方程的不变群和最优对称，再对板方程进行化约降阶，从而获得了方程的部分显式精确解。
리군이론적대칭분석상용우간화미분방정적구해，병차피유효지용우해결비선성문제。본문이용경전적리군분석방법토론일류재공정화물리영역유착엄범응용적이유형식판진동적사계편미분방정적최우대칭화정학해。수선，이용무궁소생성원방법구득방정적불변군화최우대칭，재대판방정진행화약강계，종이획득료방정적부분현식정학해。
Symmetry analysis of Lie group theory can be used to simplify a system of differen-tial equations, and plays an important role for solving non-linear problems. In this paper, the classical Lie symmetry analysis is employed to discuss a class of four-order partial differential equations of plate motion in two-dimensions, which is widely used in engineering and physical sciences. By applying infinitesimal generator, we obtain the invariant group and the optimal system of plate equation. In addition, we derive some exact solution explicitly by similarity reduction of plate equation.