article · Physica Scripta
This research investigates the complex structured fractional perturbed Gerdjikov-Ivanov equation, a mathematical model that describes the propagation of optical pulses subject to perturbation effects. The model applies directly to light transmission in optical fibres, particularly photonic crystal fibres. By applying the modified extended direct algebraic method, which has not previously been used on this specific equation, the investigation establishes new and unique optical soliton solutions. The resulting solutions encompass a hierarchy of travelling waves, including singular kink, periodic, solitary kink, and rogue-shaped solitons. Selected solutions are examined visually through graphical representations based on specific numerical parameters. These outcomes introduce novel soliton varieties to the theoretical framework and illustrate how such waves interact to influence the overall dynamical behaviour of the optical system.
Understanding how light pulses travel through optical fibres without losing their shape is essential for modern telecommunications. By identifying new mathematical solutions for pulse propagation under perturbation effects, this work deepens theoretical insight into how stable optical signals behave inside specialized components such as photonic crystal fibres.
The research relates to pulse propagation in optical fibres and photonic crystal fibres, which are relevant to optical telecommunications and laser engineering. However, the abstract presents purely theoretical and mathematical derivations accompanied by graphical parameter analyses. Because no physical testing, experimental validation, or hardware implementations are reported, this work represents very early-stage foundational research with no immediate commercial pathway.
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Abstract In this work, we examine the complex structured Fractional Perturbed Gerdjikov-Ivanov equation (FPGIE), which describes the propagation of optical pulses with perturbation effects. This model finds applications in optical fibers, especially in photonic crystal fibers. We are discovered novel and unique optical soliton solutions using the modified Extended Direct Algebraic Method (mEDAM), which has never been used with this model previously. As a result, a hierarchy of traveling wave solutions including singular kink, periodic, solitary kink, and rogue-shaped soliton solutions, etc., are derived. Some obtained solutions are discussed graphically based on numerical values of some parameters related to the solution. The results add new and unique soliton types to the model and demonstrate how they interact and impact the system’s overall dynamics.
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DOI: 10.1088/1402-4896/ad241b
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