论文标题
一些与最大对称性相关的变分原理。第2部分：一般情况
Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case
论文作者
论文摘要
在本文中，研究了整个线性和非线性对称性的最大对称性方程，并以显式形式给出了各类的线性和非线性方程。所获得的所有主要结果均作为一般顺序方程的定理或猜想。关于不同的拉格朗日人的存在对称性的讨论也是最常见和最容易获得的，也是进行的。与前者的Lagrangian相比，这导致了显着不同的结果。后一种分析还产生了有关任何线性或非线性方程的变异对称代数的更一般结果
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations
