Integrable equations with Ermakov–Pinney nonlinearities and Chiellini damping
"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 solution...
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2015 |
| Country: | México |
| Institution: | Instituto Potosino de Investigación Científica y Tecnológica |
| Repository: | Repositorio Institucional del IPICYT |
| Language: | English |
| OAI Identifier: | oai:ipicyt.repositorioinstitucional.mx:1010/899 |
| Online Access: | http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/868 http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/899 |
| Access Level: | Open access |
| Keyword: | info:eu-repo/classification/Autor/Dissipative Ermakov-Pinney equation info:eu-repo/classification/Autor/Chiellini damping info:eu-repo/classification/Autor/Reid nonlinearities info:eu-repo/classification/Autor/Abel equation info:eu-repo/classification/cti/1 |
| Summary: | "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) = Ω20(v − v2) and show that it leads to an integrable hyperelliptic case." |
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