2018年5月1日
Nonintegrability of Parametrically Forced Nonlinear Oscillators
Regular and Chaotic Dynamics
- ,
- 巻
- 23
- 号
- 3
- 開始ページ
- 291
- 終了ページ
- 303
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1134/S156035471803005X
- 出版者・発行元
- Pleiades Publishing
We discuss nonintegrability of parametrically forced nonlinear oscillators which are represented by second-order homogeneous differential equations with trigonometric coefficients and contain the Duffing and van der Pol oscillators as special cases. Specifically, we give sufficient conditions for their rational nonintegrability in the meaning of Bogoyavlenskij, using the Kovacic algorithm as well as an extension of the Morales–Ramis theory due to Ayoul and Zung. In application of the extended Morales–Ramis theory, for the associated variational equations, the identity components of their differential Galois groups are shown to be not commutative even if the differential Galois groups are triangularizable, i. e., they can be solved by quadratures. The obtained results are very general and reveal their rational nonintegrability for the wide class of parametrically forced nonlinear oscillators. We also give two examples for the van der Pol and Duffing oscillators to demonstrate our results.
- ID情報
-
- DOI : 10.1134/S156035471803005X
- ISSN : 1468-4845
- ISSN : 1560-3547
- SCOPUS ID : 85048075748