Artículos de revistas
Integrable equations with Ermakov–Pinney nonlinearities and Chiellini damping
Autor
HARET CODRATIAN ROSU
Institución
Resumen
"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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