An Analytic Technique for the Solutions of Nonlinear Oscillators with Damping Using the Abel Equation - Ghose-Choudhury, A; Guha, Partha (Discontinuity, Nonlinearity, and Complexity, 2026)
Using the Chiellini condition for integrability we derive explicit solutions for a generalized system of Riccati equations x+αx2n+1x+x4n+3 = 0 by reduction to the first-order Abel equation assuming the parameter α ≥ 2 2(n+1). The technique, which was proposed by Harko et al, involves use of an auxiliary system of first-order differential equations sharing a common solution with the Abel equation. In the process analytical proofs of some of the conjectures made earlier on the basis of numerical investigations in [1] is provided.