Published November 18, 2021
The University Department of Mathematics is pleased to announce that Elohim Fonseca dos Reis and Asela Abeya are each recipients of the Doctoral Dissertation Fellowship for the Spring Semester 2022. The award recognizes outstanding research by our graduate students.
Asela Abeya Ranasinghe Mudiyanselage, Graduate Student, UB Mathematics
Draft Dissertation: Nonlinear Schrodinger systems with non-zero background
Abstract: Nonlinear waves are ubiquitous in nature, and are described by nonlinear wave equations, which are nonlinear partial differential equations of evolution type. Scalar, vector and matrix nonlinear Schrodinger (NLS) equations are universal models for the evolution of weakly nonlinear dispersive wave trains. As such, these equations appear in many physical contexts, such as deep water waves, nonlinear optics, acoustics, and Bose-Einstein condensation. These equations are also relevant for describing modulational instability and the formation of rogue waves. It is well known that these equations are completely integrable infinite-dimensional Hamiltonian systems, and possesses an infinite number of conserved quantities. As a result, the initial value problem can in principle be solved by the inverse scattering transform (IST), a nonlinear analogue of the Fourier transform. When available, the IST provides an effective tool to study the behavior of solutions. However, the formulation of the IST is still in some cases an open problem.
For further details contact the author, Asela Abeya Ranasinghe Mudiyanselage, email@example.com
Elohim Fonseca dos Reis, Graduate Student, UB Mathematics