Self-localized solitons of a q-deformed quantum system

Cihan Bayındır*, Azmi Ali Altintas, Fatih Ozaydin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

Beyond a pure mathematical interest, q-deformation is promising for the modeling and interpretation of various physical phenomena. In this paper, we numerically investigate the existence and properties of the self-localized soliton solutions of the nonlinear Schrödinger equation (NLSE) with a q-deformed Rosen–Morse potential. By implementing a Petviashvili method (PM), we obtain the self-localized one and two soliton solutions of the NLSE with a q-deformed Rosen–Morse potential. In order to investigate the temporal behavior and stabilities of these solitons, we implement a Fourier spectral method with a 4th order Runge–Kutta time integrator. We observe that the self-localized one and two solitons are stable and remain bounded with a pulsating behavior and minor changes in the sidelobes of the soliton waveform. Additionally, we investigate the stability and robustness of these solitons under noisy perturbations. A sinusoidal monochromatic wave field modeled within the frame of the NLSE with a q-deformed Rosen–Morse potential turns into a chaotic wavefield and exhibits rogue oscillations due to modulation instability triggered by noise, however, the self-localized solitons of the NLSE with a q-deformed Rosen–Morse potential are stable and robust under the effect of noise. We also show that soliton profiles can be reconstructed after a denoising process performed using a Savitzky–Golay filter.

Original languageEnglish
Article number105474
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume92
DOIs
Publication statusPublished - Jan 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Funding

F.O. acknowledges the financial support of Tokyo International University Personal Research Fund.

FundersFunder number
Tokyo International University

    Keywords

    • q-Deformed nonlinear Schrödinger equation
    • Rogue waves
    • Rosen–Morse potential
    • Self-localized solitons

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