Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
5-15-2015
Abstract/Description
We introduce a special type of dissipative Ermakov–Pinney equations of the form v_ζζ+g(v)v_ζ+h(v)=0, where h(v)=h_0(v)+cv^{-3} and the nonlinear dissipation g(v) is based on the corresponding Chiellini integrable Abel equation. When h_0(v) is a linear function, h_0(v)=λ^2v, 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)=Ω_0^2(v-v^2) and show that it leads to an integrable hyperelliptic case.
Publication Title
Applied Mathematics and Computation
DOI
https://doi.org/10.1016/j.amc.2015.02.037
Publisher
Elsevier
Scholarly Commons Citation
Mancas, S., & Rosu, H. C. (2015). Integrable Equations with Ermakov-Pinney Nonlinearities and Chiellini Damping. Applied Mathematics and Computation, 259(). https://doi.org/10.1016/j.amc.2015.02.037
