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arXiv · 2608.13828

A family of non-autonomous hybrid Lienard oscillators based on a parametrically extended commutative factorization

J. de la Cruz·H. C. Rosu·G. Gonzalez·O. Cornejo-Perez
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Abstract

We introduce a class of nonautonomous nonlinear oscillator equations of mixed Li\'{e}nard type that arises from a parametric deformation of the commutative factorization procedure applied to second-order ordinary differential equations with periodic solutions. Their solutions, in particular the isochronous waveforms, are obtained in closed form through a Riccati reduction scheme for the power-law choice of the factorization function, $\phi(x)=kx^{q}$, $k\in \mathbb{R}$, and $q\in\mathbb{N}$, corresponding to the so-called modified Emden oscillators, and do not depend on the arbitrary deformation parameter $A_1$. The variational structure of the equation is characterised by a Lagrangian supplemented with a generalised Rayleigh dissipation function that contains a non-standard cubic term in $\dot{x}$. We also show that multiplying the equation of motion by the Jacobi multiplier $M(x)=x^{-2A_1}$ a position-dependent-mass (PDM) form is obtained with related friction and restoring force.

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J. de la Cruz, H. C. Rosu, G. Gonzalez, O. Cornejo-Perez. 2026-08-13. A family of non-autonomous hybrid Lienard oscillators based on a parametrically extended commutative factorization. https://arxiv.org/abs/2608.13828

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