Generalized damped Milne-Pinney equation and Chiellini method
Supriya Mukherjee, A. Ghose Choudhury, Partha Guha
TL;DR
This paper applies the Chiellini integrability method to solve various generalized damped Milne-Pinney equations, including the damped Ermakov-Painlevé II and dissipative variants, expanding solution techniques for nonlinear differential equations.
Contribution
It introduces the use of the Chiellini method to find solutions for new classes of damped Milne-Pinney type equations, broadening analytical approaches.
Findings
Solutions for damped Ermakov-Painlevé II equation derived
Generalized dissipative Milne-Pinney equations solved
Enhanced understanding of nonlinear damped oscillator equations
Abstract
We adopt the Chiellini integrability method to find the solutions of various generalizations of the damped Milne-Pinney equations. In particular, we find the solution of the damped Ermakov-Painlev\'e II equation and generalized dissipative Milne-Pinney equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Nonlinear Photonic Systems