EXACT SOLUTIONS OF THE (1+1)-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION VIA A NOVEL ANALYTICAL APPROACH

Khaled Mahdi (), Muhammad Bilal (), Seham Sh. Tantawy, Salah Boulaaras (), Alhanouf Alburaikan () and Hamiden Abd El-Wahed Khalifa ()
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Khaled Mahdi: Department of Physics, Faculty of Sciences, University of M’Sila, M’Sila, Algeria
Muhammad Bilal: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Seham Sh. Tantawy: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Alhanouf Alburaikan: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Hamiden Abd El-Wahed Khalifa: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-20

Abstract: This study investigates the (1+1)-dimensional chiral nonlinear Schrödinger (NLS) equation, crucial in nuclear physics for modeling chiral soliton propagation. The Extended Direct Algebraic Method (EDAM) is employed to derive a diverse range of exact solutions, including periodic, solitary, dark, bright, mixed trigonometric, hyperbolic, and rational wave solutions. These solutions provide valuable insights into the complex behavior of chiral nonlinear systems. A sensitivity analysis assesses the impact of initial condition and parameter perturbations on solution stability, highlighting the robustness and reliability of the obtained solutions. The findings contribute significantly to understanding chiral NLS equations, with potential applications in Ultrafast signal routing systems, Optical communication, Nonlinear optics, Condensed matter physics. This research advances theoretical knowledge and provides a solid foundation for future studies on chiral nonlinear systems. The exact solutions obtained can be used to model and analyze complex phenomena in various fields, demonstrating the versatility and efficacy of the mEDAM technique.

Keywords: Nonlinear Schrödinger Equation; Extended Direct Algebraic Method; Exact Solutions; Fractional Derivatives; Nonlinear Systems; Algorithms (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401796

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