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Explicit Construction of First Integrals by Singularity Analysis in Nonlinear Dynamical Systems

Abstract : The Painlevé and weak Painlevé conjectures have been used widely to identify new integrable nonlinear dynamical systems. The calculation of the integrals relies though on methods quite independent from Painlevé analysis. This paper proposes a new explicit algorithm to build the first integrals of a given set of nonlinear ordinary differential equations by exploiting the information provided by the Painlevé-Laurent series representing the solution in the neighbourhood of a movable singularity. The algorithm is based on known theorems from the theory of singularity analysis. Examples are given of the explicit construction of the first integrals in nonlinear Hamiltonian dynamical systems with a polynomial potential, and in generalized Volterra systems.
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Submitted on : Monday, October 24, 2022 - 12:19:59 PM
Last modification on : Thursday, November 10, 2022 - 12:20:05 PM

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Christos Efthymiopoulos, Tassos Bountis, Thanos Manos. Explicit Construction of First Integrals by Singularity Analysis in Nonlinear Dynamical Systems. 1st International Conference "From Scientific Computing to Computational Engineering", 1st IC-SCCE, Laboratory of Fluid Mechanics and Energy (LFME), Sep 2004, Athènes, Greece. 7 p. ⟨hal-03818547⟩

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