On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations

Dmitry I. Sinelshchikov and Nikolay A. Kudryashov

Applied Mathematics and Computation, 2017, vol. 307, issue C, 257-264

Abstract: We study a family of the Liénard-type equations, which can be transformed via the generalized Sundman transformations into a particular case of Painlevé–Gambier equation XXVII. We show that this equation of the Painlevé–Gambier type admits an autonomous Lagrangian, Jacobi last multiplier and first integral. As a consequence, we obtain that the corresponding family of Liénard-type equations also admits a time-independent Lagrangian, Jacobi last multiplier and first integral. We also construct the general analytical and singular solutions for members of this family of Liénard-type equations by virtue of the generalized Sundman transformations. To demonstrate applications of our results we consider several examples of the Liénard-type equations, with a generalization of the modified Emden equation among them, and construct their autonomous Lagrangians, Jacobi last multipliers and first integral as well as their general analytical solutions.

Keywords: Liénard-type equations; Sundman transformations; Lagrangians; Jacobi multipliers (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:307:y:2017:i:c:p:257-264

DOI: 10.1016/j.amc.2017.03.010

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