Article
Integrable Equations with Ermakov-Pinney Nonlinearities and Chiellini Damping
Applied Mathematics and Computation
(2015)
Abstract
We introduce a special type of dissipative Ermakov–Pinney equations of the form vζζ+g(v)vζ+h(v)=0, where h(v)=h0(v)+cv-3 and the nonlinear dissipation g(v) is based on the corresponding Chiellini integrable Abel equation. When h0(v) is a linear function, h0(v)=λ2v, general solutions are obtained following the Abel equation route. Based on particular solutions, we also provide general solutions containing a factor with the phase of the Milne type. In addition, the same kinds of general solutions are constructed for the cases of higher-order Reid nonlinearities. The Chiellini dissipative function is actually a dissipation-gain function because it can be negative on some intervals. We also examine the nonlinear case h0(v)=Ω02(v-v2) and show that it leads to an integrable hyperelliptic case.
Disciplines
Publication Date
May 15, 2015
DOI
https://doi.org/10.1016/j.amc.2015.02.037
Citation Information
S.C. Mancas and Haret C. Rosu. "Integrable Equations with Ermakov-Pinney Nonlinearities and Chiellini Damping" Applied Mathematics and Computation Vol. 259 (2015) p. 1 - 11 Available at: http://works.bepress.com/stefani_mancas/104/