We examine the analytical structure of the nonlinear Lienard oscillator and show that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized momentum-dependent mass system, the other Hamiltonian also reflects a similar feature in the mass function and also depicts an isotonic character. We solve for such a Hamiltonian and give the complete solution in terms of a confluent hypergeometric function. (C) 2015 AIP Publishing LLC.

B BAGCHI

A GHOSE CHOUDHURY

PARTHA GUHA

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

On quantized Liénard oscillator and momentum dependent mass

Journal of Mathematical Physics

One of the less well-understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Liénard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines. © 2015 World Scientific Publishing Company.

Modern Physics Letters A

Exploring branched Hamiltonians for a class of nonlinear systems

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 propagation dynamics is numerically studied and the sensitivity to the PDM-index is noted. Remarkable transitions from a limit cycle to chaos through period doubling and from a chaotic to a regular motion through intermediate periodic and chaotic routes are demonstrated. © 2013 IOP Publishing Ltd.

Journal of Physics A: Mathematical and Theoretical

Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech(2)-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.

Position-dependent mass models and their nonlinear characterization

A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.

Journal	Journal of Mathematical Physics
Publisher	AMER INST PHYSICS
ISSN	0022-2488