Differential Invariants and Application to Riccati-Type Systems
Mathematical Physics
2007-05-23 v1 Differential Geometry
Group Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@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}
}
Comments
12 pages