| Инд. авторы: | Medvedev S., Vaseva I., Chekhovskoy I., Fedoruk M. |
| Заглавие: | Exponential fourth order schemes for direct Zakharov-Shabat problem |
| Библ. ссылка: | Medvedev S., Vaseva I., Chekhovskoy I., Fedoruk M. Exponential fourth order schemes for direct Zakharov-Shabat problem // Optics Express. - 2020. - Vol.28. - Iss. 1. - P.20-39. - ISSN 1094-4087. |
| Внешние системы: | DOI: 10.1364/OE.377140; РИНЦ: 43226027; SCOPUS: 2-s2.0-85078065570; WoS: 000509352500002; |
| Реферат: | eng: Nowadays, improving the accuracy of computational methods to solve the initial value problem of the Zakharov-Shabat system remains an urgent problem in optics. In particular, increasing the approximation order of the methods is important, especially in problems where it is necessary to analyze the structure of complex waveforms. In this work, we propose two finite-difference algorithms of fourth order of approximation in the time variable. Both schemes have the exponential form and conserve the quadratic invariant of Zakharov-Shabat system. The second scheme allows applying fast algorithms with low computational complexity (fast nonlinear Fourier transform). © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.
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| Ключевые слова: | Initial value problems; Mathematical transformations; Approximation orders; Exponential form; Finite-difference algorithms; Fourth-order scheme; Low computational complexity; Nonlinear fourier transforms; Quadratic invariant; Urgent problems; Approximation algorithms; Computational efficiency; |
| Издано: | 2020 |
| Физ. характеристика: | с.20-39 |
