Graduation Semester and Year
2008
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Tuncay Aktosun
Abstract
The nonlinear Schrödinger (NLS) equation describes wave propagation in optical fibers, and it is one of the most well-known nonlinear partial differential equations. In 1972 Zakharov and Shabat introduced a powerful method (known as the inverse scattering transform) to solve the initial-value problem for the NLS equation. Due to mathematical and technical difficulties, this method has been available mainly in the case where the multiplicity of each bound state is one. In our research we remove that restriction and generalize the inverse scattering transform for the NLS equation to the case where the multiplicity of each bound state is arbitrarily chosen.
Disciplines
Mathematics | Physical Sciences and Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Busse, Theresa Nicole, "Generalized Inverse Scattering Transform For The Nonlinear Schrödinger Equation" (2008). Mathematics Dissertations. 89.
https://mavmatrix.uta.edu/math_dissertations/89
Comments
Degree granted by The University of Texas at Arlington