Аннотация:
The life and career of the great French mathematician and politician Paul Painlevé is described. His contribution to the analytical theory of nonlinear differential equations was significant. The paper outlines the achievements of Paul Painlevé and his students in the investigation of an interesting class of nonlinear second-order equations and new equations defining a completely new class of special functions, now called the Painlevé transcendents. The contribution of Paul Painlevé to the study of algebraic nonintegrability of the N-body problem, his remarkable observations in mechanics, in particular, paradoxes arising in the dynamics of systems with friction, his attempt to create the axiomatics of mechanics and his contribution to gravitation theory are discussed.
\RBibitem{BorKud14}
\by Alexey~V.~Borisov, Nikolay~A.~Kudryashov
\paper Paul Painlevé and His Contribution to Science
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 1
\pages 1--19
\mathnet{http://mi.mathnet.ru/rcd89}
\crossref{https://doi.org/10.1134/S1560354714010018}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000333239100001}
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https://www.mathnet.ru/rus/rcd89
https://www.mathnet.ru/rus/rcd/v19/i1/p1
Эта публикация цитируется в следующих 19 статьяx:
Muhammad Amir, Jamil Abbas Haider, Shahbaz Ahmad, Sana Gul, Asifa Ashraf, “Approximate Solution of Painlevé Equation I by Natural Decomposition Method and Laplace Decomposition Method”, Acta Mechanica et Automatica, 17:3 (2023), 417
Nikolay A. Kudryashov, “Lax Pairs and Rational Solutions of Similarity Reductions for
Kupershmidt and Sawada – Kotera Hierarchies”, Regul. Chaotic Dyn., 26:3 (2021), 271–292
Kudryashov N.A., “Lax Pairs For One of Hierarchies Similar to the First Painleve Hierarchy”, Appl. Math. Lett., 116 (2021), 107003
Nikolay A. Kudryashov, “Lax Pairs and Special Polynomials Associated with Self-similar Reductions of Sawada – Kotera and Kupershmidt Equations”, Regul. Chaotic Dyn., 25:1 (2020), 59–77
Nikolay A. Kudryashov, “Rational Solutions of Equations Associated with the Second Painlevé Equation”, Regul. Chaotic Dyn., 25:3 (2020), 273–280
Ahmad H., Khan T.A., Yao Sh.-W., “Numerical Solution of Second Order Painleve Differential Equation”, J. Math. Comput. Sci.-JMCS, 21:2 (2020), 150–157
Nikolay A. Kudryashov, “Rational and Special Solutions for Some Painlevé Hierarchies”, Regul. Chaotic Dyn., 24:1 (2019), 90–100
N. A. Kudryashov, “On Integrability of the FitzHugh – Rinzel Model”, Rus. J. Nonlin. Dyn., 15:1 (2019), 13–19
N. A. Kudryashov, “Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy”, Appl. Math. Comput., 350 (2019), 323–330
N. A. Kudryashov, “The Painlevé approach for finding solitary wave solutions of nonlinear nonintegrable differential equations”, Optik, 183 (2019), 642–649
M. B. Hubert, M. Justin, N. A. Kudryashov, G. Betchewe, Douvagai, S. Y. Doka, “Solitons in thin-film ferroelectric material”, Phys. Scr., 93:7 (2018), 075201
Nikolay A. Kudryashov, “Asymptotic and Exact Solutions of the FitzHugh–Nagumo Model”, Regul. Chaotic Dyn., 23:2 (2018), 152–160
Nikolay A. Kudryashov, “Exact Solutions and Integrability of the Duffing–Van der Pol Equation”, Regul. Chaotic Dyn., 23:4 (2018), 471–479
N. A. Kudryashov, D. I. Sinelshchikov, “On the Integrability Conditions for a Family of Liénard-type Equations”, Regul. Chaotic Dyn., 21:5 (2016), 548–555
A. R. Champneys, P. L. Varkonyi, “The Painlevé paradox in contact mechanics”, IMA J. Appl. Math., 81:3, SI (2016), 538–588
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions”, Regul. Chaotic Dyn., 20:4 (2015), 486–496
Nikolay A. Kudryashov, “Analytical Solutions of the Lorenz System”, Regul. Chaotic Dyn., 20:2 (2015), 123–133
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “Special Solutions of a High-order Equation for Waves in a Liquid with Gas Bubbles”, Regul. Chaotic Dyn., 19:5 (2014), 576–585
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