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Abundant optical soliton solutions to the Kudryashov equation and its modulation instability analysis

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Abstract

This study investigate the Kudryashov equation, which is used to describe the propagation pulses in optical fibers. The aim of this study is to find closed-form wave solutions using the new modified generalized Riccati equation mapping method. By employing the proposed method, a range of new optical solutions with distinct shapes including dark, bright, combined dark-bright, singular periodic solutions are attained. These solutions are integrated with physical parameters and exhibit special waveform characteristics under specific constraints. The modulation instability analysis of the governing model is also presented. To illustrate the propagation of selected exact solutions, graphical representations in 2D, and 3D are provided with various parametric values. Additionally, the impact of the time parameter and the non-linearity degree n are also presented. It can be convincingly stated that the employed method is remarkably efficient and achieves significant success in discovering exact solutions for nonlinear partial differential equations.

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  1. Department of Mathematics, College of Science, University of Zakho, Zakho, Iraq

    Karmina K. Ali

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  1. Karmina K. Ali
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KKA: Conceptualization, Formal analysis, Writing—original draft, Writing—review and editing.

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Correspondence to Karmina K. Ali.

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Ali, K.K. Abundant optical soliton solutions to the Kudryashov equation and its modulation instability analysis. Opt Quant Electron 56, 129 (2024). https://doi.org/10.1007/s11082-023-05653-4

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