期刊
PHYSICS LETTERS A
卷 384, 期 26, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.physleta.2020.126655
关键词
Rayleigh-like oscillators; Integrability; Nonlocal transformations
资金
- Russian Science Foundation [19-71-10003]
- Laboratory of Dynamical Systems and Applications NRU HSE, of the Ministry of science and higher education of the RF [075-15-2019-1931]
- Russian Science Foundation [19-71-10003] Funding Source: Russian Science Foundation
In this work we consider a family of nonlinear oscillators that is cubic with respect to the first derivative. Particular members of this family of equations often appear in numerous applications. We solve the linearization problem for this family of equations, where as equivalence transformations we use generalized nonlocal transformations. We explicitly find correlations on the coefficients of the considered family of equations that give the necessary and sufficient conditions for linearizability. We also demonstrate that each linearizable equation from the considered family admits an autonomous Liouvillian first integral, that is Liouvillian integrable. Furthermore, we demonstrate that linearizable equations from the considered family does not possess limit cycles. Finally, we illustrate our results by two new examples of the Liouvillian integrable nonlinear oscillators, namely by the Rayleigh-Duffing oscillator and the generalized Duffing-Van der Pol oscillator. (C) 2020 Elsevier B.V. All rights reserved.
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