Solutions of an extended Duffing-van der Pol equation with variable coefficients
Exactly Solvable and Integrable Systems
2026-02-16 v3 Mathematical Physics
math.MP
Abstract
In this work, exact solutions of the nonlinear cubic-quintic Duffing-van der Pol oscillator with variable coefficients are obtained. Two approaches have been applied, one based on the factorization method combined with the Field Method, and a second one relying on Painlev\'e analysis. Both procedures allow us to find the same exact solutions to the problem. The Lagrangian formalism for this system is also derived. Moreover, some examples for particular choices of the time-dependent coefficients, and their corresponding general and particular exact solutions are presented.
Keywords
Cite
@article{arxiv.2407.19788,
title = {Solutions of an extended Duffing-van der Pol equation with variable coefficients},
author = {O. Cornejo-Pérez and P. Albares and J. Negro},
journal= {arXiv preprint arXiv:2407.19788},
year = {2026}
}
Comments
Accepted manuscript version. Published in Physica D (2025)