In this paper, the Pad e approximation is used to improve the Adomian decomposition method (ADM) for solving the Schrödinger equation that is affected by damping term and arises in optical fibers. This equation has been solved in two cases when the damping limit vanishes and when the damping coefficient is zero. The preceding equation is an initial value problem with a rational initial condition, and the solution by the ADM is a finite series with unknown closed form. As a result, the Pad ?e ADM found the semi-analytical solution as rogue wave in the long domain with very small error. The accuracy of the Pad e Adomian decomposition method (PADM) is discussed. The case of the damping limit remains,(i.e. the damping coefficient is non-zero) is an equation that non- Integrable. As a result, the equation is solved differently by slightly changing in the scheme of PADM.

Author: Fatimah Al-zobidi

Published in: Ireland International Conference on Education (IICE-2022)

  • Date of Conference: 26-28 April 2022
  • DOI: 10.20533/IICE.2022.0016
  • ISBN: 978-1-913572-46-4
  • Conference Location: Virtual (Dún Laoghaire, Ireland)