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.
Original language | American English |
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Journal | Applied Mathematics and Computation |
Volume | 259 |
DOIs | |
State | Published - May 15 2015 |
Disciplines
- Applied Mathematics