College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Determining and Studying the Essential Conditions for Calculating the Solutions of Continuous Manakov System “The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Determining and Studying the Essential Conditions for Calculating the Solutions of Continuous Manakov System “,On Thursday, October 13, 2022, 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. The aim of this thesis, presented by the Master student Haitham Hazim Hamed in the Department of Mathematics, is to study and determine the necessary condition of obtaining soliton solutions in multi-component generalizations of the non-local reduction for nonlinear Schrödinger equation with PT-symmetry. We consider particularly square barrier potential initial conditions. This work includes: evaluating the spectral problem, introducing the Jost solutions and scattering matrix of the Zakharov-Shabat system, and determining discrete eigenvalues. As the main example, we use the Zakharov-Shabat system which corresponds to the Manakov system of nonlinear Schrödinger equation. In addition, three cases of square barrier potential corresponding to symmetric and asymmetric potentials are shown and studied. A multi-soliton configuration is shown to be allowed for multi-component non-local nonlinear Schrödinger equations of the Manakov type. Numerical simulations are used to obtain and illustrate the results that depend on solving a system of differential equations.The Viva committee was chaired by Asst. Prof. Dr. Ahmed Farouk Qassem from University of Mosul/ College of Computer Science and Mathematics and the membership of Asst. Prof. Dr. Aalan Jalal Abdel Qader, Al-Mustansiriya University/College of Education, Lecturer Dr. Suhaib Talal Hassan, University of Mosul, College of Education for Pure Sciences and under the supervision and membership of Lecturer Dr. Junaid Idris Mustafa, University of Mosul, College of Education for Pure Sciences.