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Integrable Equations With Ermakov-Pinney Nonlinearities And Chiellini Damping, S.C. Mancas, Haret C. Rosu

Publications

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 …