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Essential variables in the integrability problem of planar vector fields. (English) Zbl 1241.34018
Summary: This Letter is devoted to the integrability problem of planar nonlinear differential equations. We introduce a new method to detect local analytic integrability or to construct a singular series expansion of the first integral around a singular point for planar vector fields. The method allows to find new variables (essential variables) where the integrability problem is more feasible. The new method can be used in different context and is an alternative to all the methods developed up to now for any particular case.

34A34Nonlinear ODE and systems, general
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34C05Location of integral curves, singular points, limit cycles (ODE)
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