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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 WienerHopf factorization of matrix polynomials regardless of the partial indices of the matrix. The package can be widely used in various problems, where WienerHopf 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 language  English 

Article number  20220144 
Number of pages  25 
Journal  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 
Volume  479 
Issue number  2269 
Early online date  18 Jan 2023 
DOIs  
Publication status  Published  25 Jan 2023 
Keywords
 discrete analogue of the nonlinear Schrödinger equation
 errorfree calculation
 Padé approximation
 the ExactMPF package
 the inverse scattering transform
 WienerHopf factorization
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Supplementary material from "Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method"
Adukov, V. M. & Mishuris, G., The Royal Society, 06 Jan 2023
DOI: 10.6084/m9.figshare.c.6373073
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EffectFact: Effective Factorisation techniques for matrixfunctions: Developing theory, numerical methods and impactful applications
Mishuris, G. (PI)
01 Sept 2021 → 31 Aug 2025
Project: Externally funded research

Wolfson Visiting Fellowship  Professor Victor Eremeyev
Mishuris, G. (PI)
01 Jul 2021 → 30 Jun 2023
Project: Externally funded research