Nonlinear action of Lie groups and superposition principles for nonlinear differential equations

✍ Scribed by P. Winternitz

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 544 KB
• Volume: 114
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(82)90268-0

✦ Synopsis

Recently obtained results on superposition principles for systems of ordinary nonlinear equations are reviewed. In particular the general solution of the matrix Riccati equation is expressed in terms of five particular solutions. The study of superposition laws is related to the problem of Backlund transformations for nonlinear partial differential equations, to the problem of transforming nonlinear equations into linear ones and to the classification of primitive filtered Lie algebras.