On the integrability of Liénard I-type equations via λ-symmetries and solvable structures

A. Ruiz and C. Muriel

Applied Mathematics and Computation, 2018, vol. 339, issue C, 888-898

Abstract: For Liénard I-type equations it is proved the existence of a family of λ−symmetries such that any of them lets the computation by quadratures of a time-dependent first integral of the equation. This is achieved by using a solvable structure constructed out of the λ−symmetry and one Lie point symmetry. The first integral obtained by quadratures and the first integral associated to the Lie symmetry generator are always functionally independent and they can be therefore used to integrate completely the Liénard I-type equation.

Keywords: λ-symmetry; Liénard equation; Nonlinear oscillator; First integral; Solvable structure (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:888-898

DOI: 10.1016/j.amc.2018.07.056

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