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.

SAMIRAN GHOSH

Applied Mathematics

SWARUP PORIA

B BAGCHI

S DAS

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

Journal of Physics A: Mathematical and Theoretical

We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne's scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term f cos ωt. © 2016 AIP Publishing LLC.

Journal of Mathematical Physics

Qualitative analysis of certain generalized classes of quadratic oscillator systems

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.

On quantized Lienard oscillator and momentum dependent mass

We examine the analytical structure of the nonlinear Liénard 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. © 2015 AIP Publishing LLC.

On quantized LiÃ©nard oscillator and momentum dependent mass

In response to the comment of Mustafa (2013 J. Phys. A: Math. Theor. 46 368001) we justify our stand of considering an extended Lagrange equation involving a non-conservative force term when the particle mass varies with position. As has been known for some time, such an extended form not only takes into account the principle of virtual work applied to D'Alembert's principle but yields precisely the form of Newton's equation expected for a particle possessing a position-dependent mass. © 2013 IOP Publishing Ltd.

Reply to Comment on '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 new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wavefunctions are derived. It is shown that in a mapping to an auxiliary constant-mass Schrödinger picture one obtains one-period 'associated Lamé' well bounded by two δ-wells or δ-barriers depending on the values of the ordering parameter β. The results for bound states of this new solvable model are provided for a wide variation of the parameters. © 2006 IOP Publishing Ltd.

Journal of Physics A: Mathematical and General

Known shape-invariant potentials for the constant-mass Schrödinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its solvability imposes the form of both the deformed superpotential and the PDEM. A lot of new exactly solvable potentials associated with a PDEM background are generated in this way. A novel and important condition restricting the existence of bound states whenever the PDEM vanishes at an end point of the interval is identified. In some cases, the bound-state spectrum results from a smooth deformation of that of the conventional shape-invariant potential used in the construction. In others, one observes a generation or suppression of bound states, depending on the mass-parameter values. The corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials. © 2005 IOP Publishing Ltd.

Journal	Data powered by TypesetJournal of Physics A: Mathematical and Theoretical
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ISSN	1751-8113
Open Access	No