Differential Invariants and Application to Riccati-Type Systems
数学物理
2007-05-23 v1 微分几何
群论
math.MP
可精确求解与可积系统
摘要
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal invariant of a one-parameter group is known then a complete set of functionally independent differential invariants can be constructed via one quadrature and differentiations. Some applications of first-order differential invariants to Riccati-type systems are also presented.
引用
@article{arxiv.math-ph/0112057,
title = {Differential Invariants and Application to Riccati-Type Systems},
author = {Roman Popovych and Vyacheslav Boyko},
journal= {arXiv preprint arXiv:math-ph/0112057},
year = {2007}
}
备注
12 pages