Solutions of an extended Duffing–van der Pol equation with variable coefficients

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-04-18 DOI:10.1016/j.physd.2025.134675

O. Cornejo-Pérez , P. Albares , J. Negro

引用次数: 0

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 Painlevé 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.

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变系数扩展Duffing-van der Pol方程的解

本文给出了变系数非线性三五次Duffing-van der Pol振子的精确解。采用了两种方法，一种是基于因式分解法与场法相结合的方法，另一种是基于painlevleve分析的方法。这两种方法都能使我们找到问题的完全相同的解。导出了该系统的拉格朗日形式。此外，还给出了时变系数选择的具体例子，以及相应的一般精确解和特精确解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.