Method for Solving Systems of Differential Equations with Application in Nonlinear Optics

Aneliya Dakova*, Diana Dakova, Zara Kasapeteva, Anjan Biswas, Valeri Slavchev, Lubomir Kovachev

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The present paper focuses on a specific method for solving systems of differential equations with application in nonlinear optics. The basic system is presented by two coupled nonlinear differential equations, written in dimensionless form, which govern the propagation of light pulses in optical fibers. The mathematical algorithm is described in detail in the article. The system is analytically solved. The obtained solutions of the equations are in the form of special functions - Jacobi elliptic delta function. They determine the periodical energy exchange between light pulses. The mathematical method can be applied for pulses with arbitrary initial intensities, generalized phase and wave number mismatch.

Original languageEnglish
Title of host publicationApplications of Mathematics in Engineering and Economics, AMEE 2021
Subtitle of host publicationProceedings of the 47th International Conference "Applications of Mathematics in Engineering and Economics"
EditorsVesela Pasheva, Nedyu Popivanov, George Venkov
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735443969
DOIs
Publication statusPublished - 6 Sep 2022
Externally publishedYes
Event47th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2021 - Sofia, Virtual, Bulgaria
Duration: 7 Jun 202113 Jun 2021

Publication series

NameAIP Conference Proceedings
Volume2505
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference47th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2021
Country/TerritoryBulgaria
CitySofia, Virtual
Period07/Jun/2113/Jun/21

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