Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method

V. M. Adukov*, G. Mishuris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

We are revisiting the problem of solving a discrete nonlinear Schrödinger equation by the inverse scattering transform method, by use of the recently developed ExactMPF package within MAPLE Software. ExactMPF allows for an exact Wiener-Hopf factorization of matrix polynomials regardless of the partial indices of the matrix. The package can be widely used in various problems, where Wiener-Hopf factorization as one of the effective mathematical tools is required, as its code has already been disclosed. The analysis presented in this paper contains not only numerical examples of its use, but is also supported by appropriate and accurate a priori estimations. The procedure itself guarantees that the ExactMPF package produces all computations arithmetically exactly, and a detailed numerical analysis of various aspects of the computational algorithm and approximation strategies is provided in the case of a finite initial impulse.

Original languageEnglish
Article number20220144
Number of pages25
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume479
Issue number2269
Early online date18 Jan 2023
DOIs
Publication statusPublished - 25 Jan 2023

Keywords

  • discrete analogue of the nonlinear Schrödinger equation
  • error-free calculation
  • Padé approximation
  • the ExactMPF package
  • the inverse scattering transform
  • Wiener-Hopf factorization

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