广义Eikonal方程的群分类
Group Classification of Generalised Eikonal Equations
摘要：
本文对一类$u_a u_a=F(t,u,u_t)$形式的一阶非线性方程组给出了一种新的群分类方法。它允许完整的解决方案的组分类问题的一类方程的功能取决于多个独立的变量，其中最高的衍生物进入非线性。研究了该类的等价群和对称代数的代数性质。考虑的一类方程提出了概括的程函和Hamilton-Jacobi方程。本文列出了这类具有对称扩展的所有非等价方程，并证明了这种非等价性。构造了新的具有宽对称群的一阶非线性方程组。
英文摘要：
A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. It allowed complete solution of the group classification problem for a class of equations for functions depending on multiple independent variables, where highest derivatives enter nonlinearly. Equivalence groups of the class under consideration and algebraic properties of the symmetry algebra are studied. The class of equations considered presents generalisation of the eikonal and Hamilton-Jacobi equations. The paper contains the list of all non-equivalent equations from this class with symmetry extensions, and proofs of such non- equivalence. New first order non-linear equations possessing wide symmetry groups were constructed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
