Integrable equations with Ermakov-Pinney nonlinearities and Chiellini damping

DOI10.1016/j.amc.2015.02.037zbMath1390.34006arXiv1301.3567OpenAlexW1998072336MaRDI QIDQ1635548

Haret C. Rosu, Stefan C. Mancas

Publication date: 7 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.3567

zbMATH Keywords

Abel equationChiellini dampingdissipative Ermakov-Pinney equationReid nonlinearities

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (6)

Exact travelling wave solutions of non-linear reaction-convection-diffusion equations—An Abel equation based approach ⋮ A class of exact solutions of the Liénard-type ordinary nonlinear differential equation ⋮ Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation ⋮ Ermakov-Lewis invariants and Reid systems ⋮ Barotropic FRW cosmologies with Chiellini damping ⋮ Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: an Abel equation based approach

Cites Work

• Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations
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• A nonlinear superposition rule for solutions of the Milne-Pinney equation
• Exact linear invariants and quantum effects in the early Universe
• Theory of the alternating-gradient synchrotron
• Nonlinearity from linearity: the Ermakov-Pinney equation revisited
• The pulsrodon in 2+1-dimensional magneto-gasdynamics: Hamiltonian structure and integrability
• APPLICATIONS OF LIE SYSTEMS IN DISSIPATIVE MILNE–PINNEY EQUATIONS
• The damped Pinney equation and its applications to dissipative quantum mechanics
• The Ermakov equation: A commentary
• A dynamic correspondence between Bose–Einstein condensates and Friedmann–Lemaître–Robertson–Walker and Bianchi I cosmology with a cosmological constant
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0

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