ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

An Analytic Technique for the Solutions of Nonlinear Oscillators with Damping Using the Abel Equation

Discontinuity, Nonlinearity, and Complexity 6(1) (2017) 65--74 | DOI:10.5890/DNC.2017.03.006

A Ghose-Choudhury$^{1}$, Partha Guha$^{2}$

$^{1}$ Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta 700009, India

$^{2}$ SN Bose National Centre for Basic Sciences JD Block, Sector III, Salt Lake Kolkata 700098, India

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Abstract

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.

Acknowledgments

The authors wish to thank Professors J. K Bhattacharjee and A. Mallik for their interest and encouragement. One of us (PG) wishes to acknowledge Professor Tudor Ratiu for his gracious hospitality at the Bernoulli Centre, EPFL during the fall semester of 2014, where part of this work was done.

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