Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Petviashvili Method for the Fractional Schr\"{o}dinger Equation   In this paper, we extend the Petviashvili method (PM) to the fractional
nonlinear Schr\"{o}dinger equation (fNLSE) for the construction and analysis of
its soliton solutions. We also investigate the temporal dynamics and
stabilities of the soliton solutions of the fNLSE by implementing a spectral
method, in which the fractional-order spectral derivatives are computed using
FFT routines, and the time integration is performed by a $4^{th}$ order
Runge-Kutta time-stepping algorithm. We discuss the effects of the order of the
fractional derivative, $\alpha$, on the properties, shapes, and temporal
dynamics of the solitons solutions of the fNLSE. We also examine the
interaction of those soliton solutions with zero, photorefractive and
q-deformed Rosen-Morse potentials. We show that for all of these potentials the
soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet
their dynamics can be altered by the different forms of the potentials
considered. The splitting and spreading dynamics of the solitons of the fNLSE
are not affected by noise. Our results also indicate that the Savitzky-Golay
filter can be used for the denoising of the solitons of the fNLSE.

12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an