论文标题
半分化双曲线类型方程的分类。三阶对称的情况
Classification of semidiscrete hyperbolic type equations. The case of third order symmetries
论文作者
论文摘要
在本文中，进行了双曲线类型的半分化方程的分类。我们研究表单$ \ frac {du_ {n+1}} {dx} = f \ left（\ frac {du_ {n}} {dx} {dx}，u_ {n+1}，u_ {n} \ right），$ u _ $ u_n（$ u__n）$ u_n（$ u_n（ud）$ u_n（$ u__），变量。该分类基于对离散和连续方向上较高对称性存在的要求。当两个方向上的对称性均为3阶时，考虑了该情况。结果，获得了所需条件的方程式列表。
In this paper, a classification of semidiscrete equations of hyperbolic type is carried out. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here is the unknown function $u_n (x)$ depends on one discrete $n$ and one continuous $x$ variables. The classification is based on the requirement for the existence of higher symmetries in the discrete and continuous directions. The case is considered when the symmetries are of order 3 in both directions. As a result, a list of equations with the required conditions is obtained.
