Generalized cofactors and nonlinear superposition principles |
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Institution: | Departament de Matemàtica, Universitat de Lleida Avda. Jaume II, 69. 25001, Lleida, Spain |
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Abstract: | 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 this paper, we present a generalization of the Darboux integrability theory based on the definition of generalized cofactors. |
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