Abstract:
The Lorenz system is considered. The Painlevé test for the third-order equation corresponding to the Lorenz model at σ≠0 is presented. The integrable cases of the Lorenz system and the first integrals for the Lorenz system are discussed. The main result of the work is the classification of the elliptic solutions expressed via the Weierstrass function. It is shown that most of the elliptic solutions are degenerated and expressed via the trigonometric functions. However, two solutions of the Lorenz system can be expressed via the elliptic functions.
\Bibitem{Kud15}
\by Nikolay A. Kudryashov
\paper Analytical Solutions of the Lorenz System
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 123--133
\mathnet{http://mi.mathnet.ru/rcd49}
\crossref{https://doi.org/10.1134/S1560354715020021}
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https://www.mathnet.ru/eng/rcd49
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This publication is cited in the following 14 articles:
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Adolfo Guillot, Handbook of Geometry and Topology of Singularities VI: Foliations, 2024, 1
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M. Molaei, “The Geometry of the Trajectories”, Int. J. Geom. Methods Mod. Phys., 17:4 (2020), 2050051
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M. V. Demina, “Classification of meromorphic integrals for autonomous nonlinear ordinary differential equations with two dominant monomials”, J. Math. Anal. Appl., 479:2 (2019), 1851–1862
L. Bougoffa, S. Al-Awfi, S. Bougouffa, “A complete and partial integrability technique of the Lorenz system”, Results Phys., 9 (2018), 712–716
A. K. Volkov, N. A. Kudryashov, “Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system”, Comput. Math. Math. Phys., 56:4 (2016), 680–687
N. A. Kudryashov, “On solutions of generalized modified Korteweg-de Vries equation of the fifth order with dissipation”, Appl. Math. Comput., 280 (2016), 39–45
N. A. Kudryashov, “From the Fermi-Pasta-Ulam model to higher-order nonlinear evolution equations”, Rep. Math. Phys., 77:1 (2016), 57–67
N. A. Kudryashov, Yu. S. Ivanova, “Painlevé analysis and exact solutions for the modified Korteweg-de Vries equation with polynomial source”, Appl. Math. Comput., 273 (2016), 377–382
N. A. Kudryashov, “Refinement of the Korteweg-de Vries equation from the Fermi-Pasta-Ulam model”, Phys. Lett. A, 379:40-41 (2015), 2610–2614
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