# 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.