https://doi.org/10.1140/epjp/s13360-025-06582-9
Regular Article
On the optical soliton solutions of the concatenation model having parabolic law with nonlocal nonlinearity and modulation instability
1
Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
2
Department of Computer Engineering, Biruni University, Istanbul, Turkey
Received:
27
February
2025
Accepted:
23
June
2025
Published online:
8
July
2025
This study investigates the concatenation model having parabolic law with nonlocal nonlinearity, which describes pulse propagation in optical fibers, and explores the effects of nonlinear and dispersive terms on pulse dynamics. The model is a concatenation of the Lakshmanan–Porsezian–Daniel and the Sasa–Satsuma equations and provides a unique framework for examining the interplay between various nonlinearities and dispersion. We derive optical soliton solutions, including bright and W-shape like solitons, using the new Kudryashov method, demonstrating the model’s capacity to support diverse soliton waveforms. Additionally, we perform a modulation instability analysis to assess the stability characteristics of the system, highlighting the influence of key parameters such as nonlinear coefficients and dispersive coefficients on the onset and growth rate of instability. The effects of these parameters on soliton behavior are extensively explored through 2D and 3D graphical representations. Our findings reveal rare solution types for this novel concatenation model, offering insights into the conditions under which MI appears and the impact of various parameters on soliton dynamics. The model’s flexibility in handling both nonlinear and dispersive effects positions it as a significant tool in optical soliton studies, with potential applications in stochastic, fractional, and bifurcation analyses for future research.
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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.
