https://doi.org/10.1140/epjst/e2013-01871-6
Review
Generating finite dimensional integrable nonlinear dynamical systems*
Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India
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Received:
22
March
2013
Revised:
3
May
2013
Published online:
11
July
2013
Abstract
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties, including quantum aspects. Particularly we concentrate on Lienard type nonlinear oscillators and their generalizations and coupled versions. Specific systems include Mathews-Lakshmanan oscillators, modified Emden equations, isochronous oscillators and generalizations. Nonstandard Lagrangian and Hamiltonian formulations of some of these systems are also briefly touched upon. Nonlocal transformations and linearization aspects are also discussed.
Based on the invited lecture delivered by M. Lakshmanan at the NCNSD – 2012.
© EDP Sciences, Springer-Verlag, 2013
