Graduation Year
2021
Document Type
Dissertation
Degree
Ph.D.
Degree Name
Doctor of Philosophy (Ph.D.)
Degree Granting Department
Mathematics and Statistics
Major Professor
Wen-Xiu Ma, Ph.D.
Committee Member
Catherine A. Bénéteau, Ph.D.
Committee Member
Mohamed Elhamdadi, Ph.D.
Committee Member
Sherwin Kouchekian, Ph.D.
Committee Member
Ivan Rothstein, Ph.D.
Keywords
Higher order nonlinear Schrodinger equation, Inverse scattering, Reverse-time, Riemann-Hilbert problem, Soliton dynamics, Soliton solution
Abstract
We first investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann-Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix. Secondly, we present the inverse scattering transform for solving a class of eight-component AKNS integrable equations obtained by a specific reduction associated with a block matrix spectral problem. The inverse scattering transform based on Riemann-Hilbert problems is presented along with a jump matrix taken to be the identity matrix to derive soliton solutions.
Scholar Commons Citation
Adjiri, Alle, "Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions" (2021). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/9647
