论文标题
Eikonal方程0.1
Eikonal Equation 0.1
论文作者
论文摘要
我们提供了一些与对称相关的文献的评论，$u_μu_μ= 0 $，$u_μu_μ= 1 $，其中较低的指定变量指定派生的索引，$μ= 0,1,2，.. ..我们将考虑这些方程的一般解决方案和对称性，以及这些方程与降低高阶PDE的关系。还提出了一些全面演示所需的新结果。特别是，我们还将考虑Eikonal方程的离散对称性等效类别的解决方案和对称解和一般解决方案的关系。我们详细描述了允许使用hodograph和初始方程的接触转换获得通用解决方案的过程。作者还需要一些新的结果来进行全面演示，特别是，对于任意数量的空间变量，eikonal方程的一般解决方案。该论文既旨在作为参考材料和手册作为参考材料。
We provide a review of some symmetry-related literature on the eikonal equations $u_μu_μ=0$,$u_μu_μ=1$, where lower indices at dependent variables designate derivatives, $μ=0,1,2,..,n$ and summation is implied over the repeated indices. We will consider general solutions and symmetries of these equations, and relations of these equations with the reduction of higher-order PDE. Some new results that were needed for the comprehensive presentation are also adduced. In particular, we will also consider discrete symmetries of the eikonal equations equivalence classes of solutions and relations of the symmetry solutions and the general solutions. We describe in detail the procedure that allowed obtaining of the general solution using hodograph and contact transformations of the initial equations. Some new results by the author that were needed for comprehensive presentation are also adduced - in particular, a general solution of the eikonal equation for an arbitrary number of space variables. The paper is intended both as reference material and as a manual.
