Petviashvili Method for the Fractional Schrödinger Equation

In this paper, we extend the Petviashvili method (PM) to fractional nonlinear Schrödinger equation (fNLSE) for construction and analysis of its soliton solutions. We also investigate temporal dynamics stabilities solutions fNLSE by implementing a spectral method, in which fractional-order derivatives are computed using FFT (Fast Fourier Transform) routines, time integration is performed 4th order Runge–Kutta time-stepping algorithm. discuss effects derivative, α, on properties, shapes, fNLSE. examine interaction those with zero, photorefractive q-deformed Rosen–Morse potentials. show that all these potentials, exhibit splitting spreading behavior, yet their can be altered different forms potentials noise considered.