First integrals and parametric solutions for equations integrable through Lie symmetries
Exactly Solvable and Integrable Systems
2015-06-26 v1
Abstract
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of ``known'' functions.
Keywords
Cite
@article{arxiv.nlin/0104074,
title = {First integrals and parametric solutions for equations integrable through Lie symmetries},
author = {Claude Géronimi and Peter Leach and Marc R. Feix},
journal= {arXiv preprint arXiv:nlin/0104074},
year = {2015}
}