Integrable Ermakov-Pinney equations with nonlinear Chiellini ‘damping’
نویسندگان
چکیده
For the constant frequency case, we introduce a special type of Ermakov-Pinney equations with nonlinear dissipation based on the corresponding Chiellini integrable Abel equation. General solutions of these equations 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. These are the first examples of integrable Ermakov-Pinney equations with nonlinear ‘damping’.
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