Self-localized solitons of a q-deformed quantum system

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