Optical solutions to the extended (3+1)-dimensional cubic-quintic nonlinear conformable Schrödinger equation via two effective algorithms

• Published in: International journal of computer mathematics Vol. 102; no. 9; pp. 1333 - 1349
• Main Authors: Salih, Mohammed S., Murad, Muhammad Amin S.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.09.2025
• Subjects: 78-10; and applied mathematics; Extended (3+1)-dimensional cubic and quartic conformable nonlinear Schrödinger equation; kudryashov auxiliary equation approach; nonlinear optics; w-shaped solitons
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2025.2492796

This study explores the extended (3+1)-dimensional cubic and quartic conformable nonlinear Schrödinger equation, which is characterized by two distinct forms of nonlocal nonlinearities and has applications in optical fibre communications. Using the Kudryashov auxiliary equation approach and the simplest equation technique, a variety of innovative optical soliton solutions have been developed. The relevance and distinct features of these solutions are highlighted through visual representations such as contour diagrams, three-dimensional models, and two-dimensional plots. The effects of the fractional order and temporal parameter are investigated in detail, providing a deeper understanding of the conformable nonlinear Schrödinger equation's dynamics. Such models have significant applications in optical fibre communications, where solitons serve as stable carriers for high-speed data transmission over long distances with minimal distortion. The algorithms developed herein are applicable to other classes of nonlinear Schrödinger equations, making them valuable tools in nonlinear optics and applied mathematics.