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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 212, Number 2, Pages 167–178
DOI: https://doi.org/10.4213/tmf10257 (Mi tmf10257) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Comparison between the QP formalism and the Painlevé property in integrable dynamical systems

T. Bountisa, L. Brenigb

a Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia
b Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
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DOI: https://doi.org/10.4213/tmf10257
Abstract: 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, QP formalism, Painlevé property.
Funding agency Grant number
Russian Science Foundation 21-71-30011
Ministry of Education and Science of the Republic of Kazakhstan AP08856381
T. Bountis acknowledges financial support under the scientific project No. 21-71-30011 of the Russian Science Foundation for Sections 1, 2 and 3 of the paper, while Sections 4 and 5 were funded by grant No. AP08856381 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, for the project of the Institute of Mathematics and Mathematical Modeling MES RK, Almaty, Kazakhstan.
Received: 24.01.2022
Revised: 01.05.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 212, Issue 2, Pages 1033–1043
DOI: https://doi.org/10.1134/S0040577922080013
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: T. Bountis, L. Brenig, “Comparison between the QP formalism and the Painlevé property in integrable dynamical systems”, TMF, 212:2 (2022), 167–178; Theoret. and Math. Phys., 212:2 (2022), 1033–1043
Citation in format AMSBIB
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\paper Comparison between the~QP formalism and the~ Painlev\'{e} property in integrable dynamical systems
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\pages 167--178
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\jour Theoret. and Math. Phys.
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\crossref{https://doi.org/10.1134/S0040577922080013}
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    • This publication is cited in the following 1 articles:
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