Generalized cofactors and nonlinear superposition principles

✍ Scribed by I.A. García; J. Giné

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 421 KB
• Volume: 16
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(03)90107-8

✦ Synopsis

It

is known from Lie's works that the only ordinary differential equation of first order in which the knowledge of a certain number of particular solutions allows the construction of a fundamental set of solutions is, excepting changes of variables, the Riccati equation. For planar complex polynomial differential systems, the classical Darboux integrability theory exists based on the fact that a sufficient number of invariant algebraic curves permits the construction of a first integral or an inverse integrating factor. In thii paper, we present a generalization of the Darboux integrability theory based on the definition of generalized cofactors.