TY - JOUR

T1 - Integrable Equations with Ermakov-Pinney Nonlinearities and Chiellini Damping

AU - Mancas, S.C.

AU - Rosu, Haret C.

AU - Mancas, Stefani

N1 - 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...

PY - 2015/5/15

Y1 - 2015/5/15

N2 - 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)=Ω02(v-v2) and show that it leads to an integrable hyperelliptic case.

AB - 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)=Ω02(v-v2) and show that it leads to an integrable hyperelliptic case.

UR - https://www.sciencedirect.com/science/article/pii/S0096300315002179

U2 - 10.1016/j.amc.2015.02.037

DO - 10.1016/j.amc.2015.02.037

M3 - Article

SN - 1873-5649

VL - 259

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -