论文标题
在线上实现Lie代数和（1+1）的新组分类 - 维度均匀的非线性klein-gordon方程
Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations
论文作者
论文摘要
本质上是概括谎言的结果，我们证明了一类（1+1）二维的非线性klein-gordon方程的触点等效群体是其点等价组的一阶延长，然后我们进行此类的完整组分类。由于将其归一化，因此在此自然应用了组分类的代数方法。使用类的等价组的特定结构，我们从本质上利用经典的谎言定理对线上的矢量字段实现lie代数的实现。这种方法使我们能够增强班级方程式对称的先前结果，并实质上简化了证明。在发现了在研究类别的等价组中，在研究中不变的外态对称扩展的病例的一系列整数特征之后，我们详尽地描述了该类别中的连续的外分节对称扩展。
Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-order prolongation of its point equivalence groupoid, and then we carry out the complete group classification of this class. Since it is normalized, the algebraic method of group classification is naturally applied here. Using the specific structure of the equivalence group of the class, we essentially employ the classical Lie theorem on realizations of Lie algebras by vector fields on the line. This approach allows us to enhance previous results on Lie symmetries of equations from the class and substantially simplify the proof. After finding a number of integer characteristics of cases of Lie-symmetry extensions that are invariant under action of the equivalence group of the class under study, we exhaustively describe successive Lie-symmetry extensions within this class.
