Bayindir, CihanAltintas, Azmi AliOzaydin, Fatih2024-05-252024-05-2520211007-57041878-727410.1016/j.cnsns.2020.1054742-s2.0-85089152535https://doi.org/10.1016/j.cnsns.2020.105474https://hdl.handle.net/20.500.14517/1590BAYINDIR, Cihan/0000-0002-3654-0469; Altintas, Azmi Ali/0000-0003-2383-4705Beyond 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.eninfo:eu-repo/semantics/openAccessq-Deformed nonlinear Schrodinger equationRosen-Morse potentialSelf-localized solitonsRogue wavesArticleQ1Q192WOS:00057949300001010