College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” On Finding Discrete Eigenvalues in Integrable Equations ”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” On Finding Discrete Eigenvalues in Integrable Equations “,

On Monday, September 4, 2023, the College staff including the respected Dean of the College, Assistant Professor Dr. Qais Ismail Ibrahim, the Honorable Scientific Associate and Administrative Associate, the Honorable Head of the Department of Mathematics, and a number of the college’s teachers were attended the viva.

In this study, presented by the Master student Dina Ammar Salih Al-Rahow in the Department of Mathematics, two models of the discrete nonlinear Manakov system are studied, the first model is called the Nonlocal Discrete Manakov System (NDMS), and the other model is called the New- Nonlocal Discrete Manakov System (NE-NDMS).

This study also includes: solving the spectral problem and finding the eigenfunctions and dispersion data. The importance of our study lies in examining the conditions that characterize the soliton. There are two cases of power functions: single and double barriers. If the Lax-operator does not have a spectrum outside or inside the unit circle, there is no soliton-type solution, which can happen in a single barrier (single barriers). On the other hand, two-site double barriers give two separate solutions. It turns out that the soliton is most likely to occur at discrete eigenvalues outside or inside the unit circle.

The Viva committee was chaired by Prof. Dr. Alaa Abdul-Raheem Ahmed / University of Mosul/ College of Education for Pure Science and the membership of Asst. Prof. Dr. Badran Jasim Salim / University of Mosul / College of Basic Education, Asst. Prof. Dr. Firas Adel Fawzi /University of Tikrit / College of Computer Science and Mathematics and under the supervision and membership of Asst. Prof. Dr. Amal Jasim Mohammed /University of Mosul, College of Education for Pure Science.