OPTICAL SOLUTIONS WITH KUDRYASHOV’S ARBITRARY TYPE OF GENERALIZED NON-LOCAL NONLINEARITY AND REFRACTIVE INDEX VIA KUDRYASHOV AUXILIARY EQUATION METHOD

Muhammad Amin Sadiq Murad, Waqas Ali Faridi, Adil Jhangeer, Mujahid Iqbal and Mubariz Garayev
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Muhammad Amin Sadiq Murad: Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq
Waqas Ali Faridi: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Adil Jhangeer: IT4Innovations, VŠB – Technical University of Ostrava, Ostrava-Poruba, Czech Republic
Mujahid Iqbal: College of Information Science and Technology, Dalian Maritime University, Dalian 116026, Liaoning, P. R. China
Mubariz Garayev: Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-15

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.

Keywords: Kudryashov Auxiliary Equation Method; Optical Solutions; Conformable Nonlinear Schrödinger Equation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401012

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