Nonintegrability of Parametrically Forced Nonlinear Oscillators

被引：0
作者：
Shoya Motonaga
Kazuyuki Yagasaki
机构：
[1] Kyoto University,Department of Applied Mathematics and Physics, Graduate School of Informatics
[2] Yoshida-Honmachi,undefined
[3] Sakyo-ku,undefined
来源：
Regular and Chaotic Dynamics | 2018年 / 23卷
关键词：
nonintegrability; nonlinear oscillator; Morales–Ramis theory; differential Galois theory; 37J30; 34C15; 70K40;
D O I：
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中图分类号：
学科分类号：
摘要：
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.
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页码：291 / 303
页数：12
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