Study of nonlinear wave equation of optical field for solotonic type results

Abstract

This paper uses the fractional perturbed Gerdjikov–Ivanov (PGI) model, a basic mathematical framework in mathematical physics and nonlinear dynamics, to examine complex wave structures using the M-fractional operator and modified Extended Direct Algebraic Method (mEDAM). We find a wide variety of new optical wave solutions, such as kink-type, dark, brilliant, periodic, combo, exponential, trigonometric, and hyperbolic solutions. our examine the dynamic behavior and free parameters of these soliton solutions using contour plots and three-dimensional charts. The uniqueness of the study is shown by the noteworthy consistency and divergence of our results from earlier answers. This work makes a substantial contribution to the PGI model’s ability to extract many solitary wave solutions. The proposed suggested method shows dependability while assessing analytical solutions for fractional differential equations. This research intends to extend mathematical approaches for solving fractional differential equations, which will enable answers to a wide range of practical scientific and engineering problems, including implications for ultrafast pulse transmission in optical fibers.

Keywords

• Fractional differential equations
• Modified Extended Direct Algebraic Method (mEDAM)
• Fractional perturbed Gerdjikov–Ivanov (PGI) model
• Nonlinear optics
• Solitary wave solutions
• Advancements in mathematical modeling