Generating Finite Dimensional Integrable Nonlinear Dynamical Systems

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.

To appear in Eur. Phys. J - ST 222, 665 (2013)

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Cited by in corpus (20)

• Contact Hamiltonian Mechanics
• Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability
• Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator
• Time-evolution of quantum systems via a complex nonlinear Riccati equation II. Dissipative systems
• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability
• Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
• Asymmetric variation of a finite mass harmonic like oscillator
• n-dimensional PDM non-linear oscillators: Linearizability and Euler-Lagrange or Newtonian invariance
• Coherent and squeezed states: introductory review of basic notions, properties and generalizations
• On the classical and quantum dynamics of a class of nonpolynomial oscillators
• $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability
• On the symmetries of a nonlinear non-polynomial oscillator
• Qualitative analysis of certain generalized classes of quadratic oscillator systems
• Liénard Type Nonlinear Oscillators and Quantum Solvability
• Dynamics of the Modified Emden and pseudo-Modified Emden Equations: position-dependent mass, invariance and exact solvability
• A Class of Isochronous and Non-Isochronous Nonlinear Oscillators
• Quantization of Liénard's nonlinear harmonic oscillator and its solutions in the framework of supersymmetric quantum mechanics
• Two-dimensional isochronous nonstandard Hamiltonian systems
• Quasi-harmonic spectra from branched Hamiltonians