Solutions of nonlinear differential and difference equations with superposition formulas

Authors
Turbiner, A Winternitz, P
Citation
A. Turbiner et P. Winternitz, Solutions of nonlinear differential and difference equations with superposition formulas, LETT MATH P, 50(3), 1999, pp. 189-201
Citations number
19
Categorie Soggetti
Physics
Journal title
LETTERS IN MATHEMATICAL PHYSICS
ISSN journal
03779017 → ACNP
Volume
50
Issue
3
Year of publication
1999
Pages
189 - 201
Database
ISI
SICI code
0377-9017(199911)50:3<189:SONDAD>2.0.ZU;2-U
Abstract
Matrix Riccati equations and other nonlinear ordinary differential equation s with superposition formulas are, in the case of constant coefficients, sh own to have the same exact solutions as their group theoretical discretizat ions. Explicit solutions of certain classes of scalar and matrix Riccati eq uations are presented as an illustration of the general results.