https://doi.org/10.1140/epjp/s13360-025-07066-6
Regular Article
The perturbed Fokas–Lenells equation with Kudryashov’s law of self-phase modulation having the spatiotemporal dispersion
1
Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
2
Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
3
Department of Computer Engineering, Biruni University, Istanbul, Turkey
4
Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey
Received:
24
August
2025
Accepted:
12
November
2025
Published online:
29
November
2025
This work focuses on applying the addendum to Kudryashov’s method to generate the soliton solutions of the perturbed Fokas–Lenells equation with Kudryashov’s law of self-phase modulation having the spatiotemporal dispersion. The presence of self-phase modulation offers a nonlinear intensity-dependent refractive index, while the spatiotemporal dispersion accounts for both temporal and spatial effects in wave propagation. We indicate the dark and bright soliton solutions through the three-dimensional, contour, and two-dimensional portraits. The physical importance of these soliton solutions is discussed, offering a greater understanding of the behavior of nonlinear waves in media characterized by both dispersive and nonlinear effects. Modulation instability (MI) analysis has a crucial role in understanding the dynamics and stability properties of nonlinear models. So, the model under consideration is comprehensively examined to assess its spatiotemporal behavior and identify relevant instability conditions. The findings of this study enhance the broader comprehension of soliton dynamics within nonlinear optical and fluid systems. These insights may have significant implications for the development of advanced communication technologies and further applications across various domains of nonlinear wave theory.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
