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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 language | English |
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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
- error-free calculation
- Padé approximation
- the ExactMPF package
- the inverse scattering transform
- Wiener-Hopf 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 matrix-functions: Developing theory, numerical methods and impactful applications
01 Sept 2021 → 31 Aug 2025
Project: Externally funded research
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