College of Computer Science and Mathematics

Discussion of Ms.C. Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Study on Exact and Approximate Solutions of Some Nonlinear Evolution “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Monday, 1 -9-2025.

Ms.C  Dissertation by Nadia Dahham Rashad Ajaj

under the supervision of Asst. prof. Dr. Mohammad Omar shaaban Mohammed  & Asst. prof. Dr. Ahmed Amer Mohammed Fawze Hassan

 This study aims to derive analytical and approximate solutions for the (1+1)-dimensional Mikhailov-Novikov-Wang system, a fifth-order nonlinear and integrable system that describes the propagation of nonlinear waves and provides new insights into the connection between integrability and water wave phenomena. Two analytical methods are used: the Sinh Gordon equation expansion method and Kudryashov’s new function method, in addition to an approximate method, the ARA-Homotopy Perturbation Method (ARA-HPM). The two analytical methods contribute to finding exact solutions by transforming the mathematical model into ordinary differential equations using the wave transform. New traveling wave solutions of various types were obtained, including, Anti-Bell-shaped Solitons Bell-shaped solitons, single soliton Solutions, and periodic Solutions. these were derived by assigning specific parameter values. Jacobi Elliptic, hyperbolic, and trigonometric functions were used to formulate these solutions. The ARA-HPM method relies on combining the Homotopy Perturbation Technique with the ARA transform. Nonlinear terms in the system are handled using He’s polynomials. The approximate solution is represented as a convergent series of easily computable terms. This method does not require discretization. Two-dimensional and three dimensional plots were presented to display the exact and approximate solutions of the MNW system resulting from the application of the proposed methods. We show the accuracy and reliability of the approximate solutions by comparing them with the exact solutions. These methods are found to be effective in producing new solutions essential for understanding the dynamics of the system. They are applicable to many nonlinear partial differential equations arising in physics.

The scientific committee included the following members:

• Dr. Saad Fawzi Jassim– Chairman

• Prof. Dr. Lamia Hazem Saadoun – Member.
• Assist . Prof. Dr. Khadr Mohammed Salih – Member.
• Prof. Dr. Mohammed Omar shaaban Mohammed – Member and supervisor.
• Prof. Dr. Ahmed Amer Mohamed Fawzi – Member and supervisor.