Self-localized solitons of a q-deformed quantum system

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Bayındır C., Altintas A. A., Ozaydin F.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.92, 2021 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 92
  • Publication Date: 2021
  • Doi Number: 10.1016/j.cnsns.2020.105474
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: q-Deformed nonlinear Schrodinger equation, Rosen-Morse potential, Self-localized solitons, Rogue waves, HARMONIC-OSCILLATOR, ROGUE WAVES, PROPAGATION, EQUATIONS, SPECTRA, ALGEBRA, BRIGHT, FORM, EVEN, ODD
  • Open Archive Collection: AVESIS Open Access Collection
  • Istanbul University Affiliated: No

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 Schrodinger 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. (C) 2020 Elsevier B.V. All rights reserved.