Solutions of Non-linear Differential and Difference Equations with Superposition Formulas
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit solutions of certain classes of scalar and matrix Riccati equations are presented as an illustration of the general results.
Keywords
Cite
@article{arxiv.solv-int/9905003,
title = {Solutions of Non-linear Differential and Difference Equations with Superposition Formulas},
author = {Alexander Turbiner and Pavel Winternitz},
journal= {arXiv preprint arXiv:solv-int/9905003},
year = {2007}
}
Comments
17 pages, REVTeX, submitted to Journ.Math.Phys