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 …

We review the general theory of the Jacobi last multipliers in geometric terms and then apply
the theory to different problems in integrability and the inverse problem for one-dimensional …

Classical dynamical systems close to a critical point are known to act as efficient sensors
due to a strongly nonlinear response. We explore such systems in the quantum regime by …

We examine some nontrivial consequences that emerge from interpreting a position-
dependent mass (PDM)-driven Duffing oscillator in the presence of a quartic potential. The …

A periodically forced Liénard system is capable of generating frequent large-amplitude
chaotic bursts for a range of system and external forcing parameter values which are known …

We extend exactly solvable model of a one-dimensional non-relativistic canonical
semiconfined quantum harmonic oscillator with a mass that varies with position to the case …

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity
dependence have received attention in the literature. For one thing, such Lagrangians have …

We investigate the connection between the linear harmonic oscillator equation and some
classes of second-order nonlinear ordinary differential equations of Liénard and generalized …

This paper addresses the dynamics of a position-dependent mass-driven Duffing-type
oscillator (PDM oscillator) subjected to periodic excitation. The approximate equation of the …

The classical quantization of a Liénard-type nonlinear oscillator is achieved by a
quantization scheme (MC Nucci. Theor. Math. Phys., 168: 994–1001, 2011) that preserves …