https://doi.org/10.1140/epjp/s13360-023-04127-6
Regular Article
Higher-order Sasa–Satsuma equation: Nucci’s reduction and soliton solutions
1
Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000, Annaba, Algeria
2
Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, 44891-63157, Rudsar-Vajargah, Iran
3
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt
4
Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, Egypt
5
Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey
Received:
18
April
2023
Accepted:
21
May
2023
Published online:
29
May
2023
This paper discusses the existence of a diverse range of novel periodic nonlinear waves in the generalized (3+1)-dimensional Sasa–Satsuma equation. This equation models the transmission of femtosecond light pulses through optical fibers, taking into account third-order dispersion, self-frequency shift, and self-steepening effects in all three spatial dimensions of the system. The article presents newly derived periodic wave solutions expressed in terms of Jacobi elliptic functions and also obtains bright and dark soliton solutions in the long-wave limit of the periodic wave solutions. Moreover, a reduction technique employed to obtain another soliton solution and first integral of the considered model. Additionally, the article highlights the necessary fiber parameters required for the existence of these structures and provides graphical illustrations of selected solutions to demonstrate their physical nature.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
