ON THE PERIODIC SOLITON SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATIONS

Rashid Ali, Devendra Kumar (), AKGÃœL Ali and Ali Altalbe
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Rashid Ali: School of Mathematical Sciences, Zhejiang Normal University, 688 Yingbin Road, Jinhua, Zhejiang 321004, P. R. China
Devendra Kumar: Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
AKGÃœL Ali: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon4Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey
Ali Altalbe: Department of Computer Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia6Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia

FRACTALS (fractals), 2024, vol. 32, issue 07n08, 1-30

Abstract: In this research, we use a novel version of the Extended Direct Algebraic Method (EDAM) namely generalized EDAM (gEDAM) to investigate periodic soliton solutions for nonlinear systems of fractional Schrödinger equations (FSEs) with conformable fractional derivatives. The FSEs, which is the fractional abstraction of the Schrödinger equation, grasp notable relevance in quantum mechanics. The proposed gEDAM technique entails creating nonlinear ordinary differential equations via a fractional complex transformation, which are then solved to acquire soliton solutions. Several 3D and contour graphs of the soliton solutions reveal periodicity in the wave profiles that offer crucial perspectives into the behavior of the system. The work sheds light on the dynamics of FSEs by displaying numerous families of periodic soliton solutions and their intricate relationships. These results hold significance not only for comprehending the dynamics of FSEs but also for nonlinear fractional partial differential equation applications.

Keywords: Fractional Schrödinger Equations; Quantum Mechanics; Closed Form Solutions; Generalized Extended Direct Algebraic Method; Analytical Method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400334

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