The University of Duhok (UOD) is pleased to announce a new publication by Dr. Muhammad Amin S. Murad, Assistant Professor in the Department of Mathematics, College of Science. The research, published in the highly respected journal Physica Scripta by IOP Publishing, presents a significant contribution to nonlinear wave analysis in optical physics and applied mathematics.

Title: “Soliton solutions of cubic-quintic-septimal nonlinear Schrödinger wave equation with conformable derivative by two distinct algorithms”

📚 Journal: Physica Scripta, Volume 99, Issue 10 (October 2024)
📅 Publication Date: 10 September 2024
🔗 DOI: https://doi.org/10.1088/1402-4896/ad75c1

🔍 Research Highlights: New Approaches to Nonlinear Wave Propagation

This study explores the evolution of optical wave beams in weakly nonlocal media through the lens of the cubic-quintic-septimal nonlinear Schrödinger equation, enhanced by a conformable derivative framework. Dr. Murad employs two powerful analytical methods:

• Kudryashov Method
• Enhanced Modified Tanh Expansion Method

Using these tools, the paper derives exact soliton solutions, including:

• Kink-type solitons
• Bell-shaped solitons
• Singular waveforms
• Dark solitons
• Traveling wave solitons

These solutions are visualized using two-dimensional, three-dimensional, and contour plots, highlighting their relevance in modeling real-world physical systems.

📈 Scientific and Strategic Relevance to UOD

This research exemplifies UOD’s commitment to advancing frontier knowledge in mathematical modeling and nonlinear science. It supports UOD’s Strategic Plan 2023–2038 by:

• Promoting cross-disciplinary applications of mathematics in physics and engineering
• Enhancing visibility of UOD scholars in international journals
  Strengthening UOD’s research reputation in nonlinear optics, a high-impact field with applications in laser systems, telecommunications, and quantum computing

🗣 Dr. Muhammad Amin S. Murad commented:

“This work underscores the power of mathematical modeling in understanding the complex behavior of light in nonlinear media. The derived soliton structures pave the way for exploring wave phenomena in quantum systems, fiber optics, and signal transmission.”

👤 About the Author

Dr. Muhammad Amin S. Murad is an Assistant Professor in the Department of Mathematics, College of Science, University of Duhok, Iraq. His research focuses on nonlinear differential equations, optical solitons, and mathematical physics.
📧 Email: [email protected]
🔗 ORCID: https://orcid.org/0000-0002-3402-1796

🌍 Broader Impact and Applications

The governing equation studied has practical implications across several advanced fields:

• Nonlinear optics: Predicting laser beam propagation in nonlinear media
• Quantum mechanics: Understanding wave-particle dynamics in confined systems
• Soliton theory: Engineering robust pulse transmission in optical fibers
• Applied mathematics: Developing methods to solve complex differential equations

The integration of higher-order nonlinearities (cubic, quintic, septimal) provides a deeper insight into wave interactions, essential for the design of advanced photonic devices.

🔍 SEO Keywords:

Cubic-quintic-septimal Schrödinger equation, conformable derivative soliton, nonlinear optics modeling, optical soliton solutions, University of Duhok mathematics, Physica Scripta publication, weak nonlocal media

📍 UOD Media & Public Relations | June 2025
✍ Prepared by: University Press Office