Solving Eigenfunctions for Rotating Nonlinear Systems
Faculty Mentor
Dr. Shijun Zheng
Location
Russell Union Ballroom
If Other was choses above, please indicate your topic area here:
Mathematical science
Type of Research
Proposed
Session Format
Poster Presentation
College
College of Science & Mathematics
Department
Mathematical Sciences
Abstract
This project studies a class of nonlinear Schrödinger equations (NLS) that model rotating quantum systems and external magnetic effects which have been studied extensively in semiclassical analysis. In particular, we consider the magnetic nonlinear Schrödinger equation in one and two spatial dimensions, focusing on its periodic forms. These equations arise in mathematical physics and are used to describe phenomena such as rotating Bose–Einstein condensates and quantum particles in magnetic fields. We investigate solutions of a one-dimensional periodic nonlinear Schrödinger equation with a rotational term. By linearizing the equation, we analyze the associated linear operator and determine its eigenvalues and eigenfunctions. The goal of this project is to better understand how rotational effects modify the asymptotic behavior, symmetry, and stability of solutions to nonlinear Schrödinger equations. Through Fourier analysis, ODE, and PDE methods, we aim to provide a clear mathematical description of how rotation affects the structure of solutions.
Program Description
.
Start Date
4-23-2026 10:00 AM
End Date
4-23-2026 12:00 PM
Recommended Citation
Jarra, Ibrahim, "Solving Eigenfunctions for Rotating Nonlinear Systems" (2026). GS4 Student Scholars Symposium. 85.
https://digitalcommons.georgiasouthern.edu/research_symposium/2026/2026/85
Solving Eigenfunctions for Rotating Nonlinear Systems
Russell Union Ballroom
This project studies a class of nonlinear Schrödinger equations (NLS) that model rotating quantum systems and external magnetic effects which have been studied extensively in semiclassical analysis. In particular, we consider the magnetic nonlinear Schrödinger equation in one and two spatial dimensions, focusing on its periodic forms. These equations arise in mathematical physics and are used to describe phenomena such as rotating Bose–Einstein condensates and quantum particles in magnetic fields. We investigate solutions of a one-dimensional periodic nonlinear Schrödinger equation with a rotational term. By linearizing the equation, we analyze the associated linear operator and determine its eigenvalues and eigenfunctions. The goal of this project is to better understand how rotational effects modify the asymptotic behavior, symmetry, and stability of solutions to nonlinear Schrödinger equations. Through Fourier analysis, ODE, and PDE methods, we aim to provide a clear mathematical description of how rotation affects the structure of solutions.
