Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 the existence and properties of the self-localized
soliton solutions of the nonlinear Schr\"{o}dinger 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 $4^{th}$ 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.

25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con