Geodesic
Comparison between the~QP formalism and the~ Painlev\'{e} property in integrable dynamical systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 167-178

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The quasipolynomial (QP) formalism and the Painlevé property constitute two distinct approaches for studying the integrability of systems of ordinary differential equations with polynomial nonlinearities. The former relies on a set of quasimonomial variable transformations, which explore the existence of hidden quasipolynomial invariants, while the latter requires that all solutions be meromorphic, expressed in the form of Laurent series in the complex time domain. In this paper, we compare the effectiveness of these approaches as independent methods for identifying integrals of motion, in many examples of polynomial dynamical systems of physical interest.
Keywords: integrable dynamical systems, Painlevé property.
Mots-clés : QP formalism 
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     author = {T. Bountis and L. Brenig},
     title = {Comparison between {the~QP} formalism and the~ {Painlev\'{e}} property in integrable dynamical systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a0/}
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T. Bountis; L. Brenig. Comparison between the~QP formalism and the~ Painlev\'{e} property in integrable dynamical systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 167-178. http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a0/