An Analytic Technique for the Solutions of Nonlinear Oscillators with Damping Using the Abel Equation
DOI:
https://doi.org/10.5890/DNC.2017.03.006Abstract
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.References
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