Eur. Phys. J. Special Topics 222, 665-688 (2013)
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

^a e-mail: lakshman.cnld@gmail.com
^b e-mail: chandru25nld@gmail.com

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.