Self-localized solitons of a q-deformed quantum system
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.
- Publication:
-
Communications in Nonlinear Science and Numerical Simulations
- Pub Date:
- January 2021
- DOI:
- 10.1016/j.cnsns.2020.105474
- arXiv:
- arXiv:2005.04082
- Bibcode:
- 2021CNSNS..9205474B
- Keywords:
-
- q-Deformed nonlinear Schrödinger equation;
- Rosen-Morse potential;
- Self-localized solitons;
- Rogue waves;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Quantum Physics
- E-Print:
- doi:10.1016/j.cnsns.2020.105474