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Integrable Equations With Ermakov-Pinney Nonlinearities And Chiellini Damping, S.C. Mancas, Haret C. Rosu
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 …
Barotropic Frw Cosmologies With Chiellini Damping, Haret C. Rosu, S.C. Mancas, Pisin Chen
Barotropic Frw Cosmologies With Chiellini Damping, Haret C. Rosu, S.C. Mancas, Pisin Chen
Publications
It is known that barotropic FRW equations written in the conformal time variable can be reduced to simple linear equations for an exponential function involving the conformal Hubble rate. Here, we show that an interesting class of barotropic universes can be obtained in the linear limit of a special type of nonlinear dissipative Ermakov–Pinney equations with the nonlinear dissipation built from Chiellini's integrability condition. These cosmologies, which evolutionary are similar to the standard ones, correspond to barotropic fluids with adiabatic indices rescaled by a particular factor and have amplitudes of the scale factors inverse proportional to the adiabatic index.