Essential variables in the integrability problem of planar vector fields |
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Authors: | Jaume Giné Xavier Santallusia |
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Institution: | Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Spain |
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Abstract: | 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. |
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Keywords: | Integrability problem Systems of nonlinear differential equations First integral |
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