OPTICAL SOLUTIONS WITH KUDRYASHOV’S ARBITRARY TYPE OF GENERALIZED NON-LOCAL NONLINEARITY AND REFRACTIVE INDEX VIA KUDRYASHOV AUXILIARY EQUATION METHOD
Muhammad Amin S. Murad, Waqas Ali Faridi, Adil Jhangeer, MUJAHID IQBAL, Mübariz Garayev
Abstract
In this paper, our focus lies in exploring the Kudryashov auxiliary equation method as a means to derive several exact solutions to a conformable nonlinear Schrödinger equation. This particular model combines Kudryashov’s arbitrary refractive index alongside two various non-local nonlinearity. Through our investigation, we unveil a plethora of new optical solutions characterized by their representation using hyperbolic and exponential functions. The present results fall into various categories, including wave, bright-dark, multi-bell-shaped, bell-shaped, and singular solitons, each offering unique insights into the behavior of light in nonlinear media. To offer a thorough insight into the scale and complexity of the constructed exact solutions, we depicted contour plots, three dimensions, and two dimensions. Additionally, we delve into the characteristic of the new soliton solutions via illustrative plots, demonstrating their evolution under different values of the time parameter and fractional order derivative. Our findings suggest that the proposed technique serves as a robust and accurate method to analyze exact solutions in a wide spectrum of Schrödinger models, whether of fractional or integer nature.