The nonlinear Schrodinger (NLS) equation is considered on a metric graph subject to the Kirchhoff boundary conditions. The most important graph configurations are of the shape: star, tadpole, periodic, dumbbell, and other bounded symmetric graphs. The project is to characterize bifurcations and stability of standing waves and to single out ground states (states of least energy for fixed mass).
Impact
This project contributes to the fundamental research on the new area of mathematical physics involving nonlinear partial differential equations in confining domains.
Student Experience
New PhD Student (Adilbek Kairzhan) at Department of Mathematics is actively involved in research on PDE on star graphs.
Countries
Germany, United States of America
Impact
Research
Institutional Partner(s)
University of Stuttgart, University of North Carolina at Chapel Hill, Texas A & M University
