(2+1)维WGC方程和Volterra格方程的Lie对称

The symmetries of the (2+1)-dimensional WGC equation and the Volterra lattice equation

离散的Lie对称约化方法是研究微分差分方程的经典方法。应用离散的Lie对称约化方法研究(2+1)维WGC方程和Volterra格方程,获得这两个方程的无限维李代数及对称。因为(2+1)维WGC方程是一个有理型的微分差分方程,所以在约化过程中需要考虑其分母的约束条件;非线性离散Volterra格方程不能直接应用离散的Lie对称约化方法,为此采取相似变换法,将其转化为可以使用其进行对称约化的方程。

Discrete Lie symmetry reduction procedure is a classical method to study the differential-difference equation. Discrete Lie symmetry reduction procedure is used to study the (2+1)-dimensional WGC equation and the Volterra lattice equation. The infinite dimensional Lie algebra and symmetry of these two equations are obtained. The (2+1)-dimensional WGC equation is a rational differential-difference equation, so it is necessary to consider the denominator constraint in the process of reduction. We can not directly apply the discrete Lie symmetry reduction procedure to the nonlinear discrete Volterra lattice equation, in order to solve this problem, we use a similar transformation method to convert it into an equation which can be used to perform symmetric reduction.