The perturbed Fokas-Lenells equation with Kudryashov's law of self-phase modulation having the spatiotemporal dispersion

Abstract

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.