Generalized Nonlinear Superposition Principles for Polynomial Planar Vector Fields∗

Abstract

In this paper we study some aspects of the integrability problem for polynomial vector fields ẋ = P (x, y), ẏ = Q(x, y). We analyze the possible existence of first integrals of the form I(x, y) = (y − g1(x))1(y − g2(x))2 · · · (y−g`(x))`h(x), where g1(x), . . . , g`(x) are unknown particular solutions of dy/dx = Q(x, y)/P (x, y), αi are unknown constants… (More)

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Cite this paper

@inproceedings{Gara2004GeneralizedNS, title={Generalized Nonlinear Superposition Principles for Polynomial Planar Vector Fields∗}, author={Isaac A. Gar{\'c}ıa and H{\'e}ctor Giacomini and Peter J. Olver}, year={2004} }