Analysis of the Nonlinear Schrodinger Equation
Department
Physics
Major
Physics
Research Advisor
Murphy, Jason
Advisor's Department
Mathematics and Statistics
Abstract
We analyze the nonlinear Schrodinger equation for application to Bose-Einstine condensates. First, we devise a rigorous mathematical model for the underlying physics. We then prove well-posedness and establish sharp bounds for solutions to the equation. Deriving a rigorous model for the dynamics of a general condensate, we then analyse several other physically interesting solutions, particularly radially symmetric and solitary wave solutions. We finally compare these results to experimental Bose-Einstein condensate results, discussing physically interesting details.
Biography
Nicholas Parris is a senior of Physics and Mathematics who has done research in Atomic physics for three years as a apart of the I.AMOR group under Dr. Daniel Fischer, an assistant professor in the MST Physics Department studying quantum gas collisions. Nicholas' research advisor for this project, Dr. Jason Murphy, is an assistant professor of the MST Mathematics Department who is an expert in the analysis of nonlinear partial differential equations.
Presentation Type
OURE Fellows Final Oral Presentation
Document Type
Presentation
Location
Missouri Room
Presentation Date
16 Apr 2019, 10:00 am - 10:30 am
Analysis of the Nonlinear Schrodinger Equation
Missouri Room
We analyze the nonlinear Schrodinger equation for application to Bose-Einstine condensates. First, we devise a rigorous mathematical model for the underlying physics. We then prove well-posedness and establish sharp bounds for solutions to the equation. Deriving a rigorous model for the dynamics of a general condensate, we then analyse several other physically interesting solutions, particularly radially symmetric and solitary wave solutions. We finally compare these results to experimental Bose-Einstein condensate results, discussing physically interesting details.
