Talk by Setenay Akduman
On May 29th, 2024, Setenay Akduman (İzmir Democracy University) gave a talk about "Nonlinear Schrödinger Equation on Infinite Metric Graphs" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
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This study deals with nonlinear Schrödinger equations (NLS) with growing potentials on sufficiently general metric graphs. Motivation for the study of NLS equation comes from nonlinear optics and fiber optics. If cables are branching, it is natural to look at quantum graphs. Assuming the linear potential is infinitely growing, we prove an existence of solutions that covers both self-focusing and defocusing cases. Our approach is variational and based on generalized Nehari manifold.
Thank Professor Alexander Pankov (Mathematics Department, Morgan State University, USA) for his guidance, remarks and comments for the occurrence of this joint work. May he rest in peace.
Akduman, S., Pankov, A., Schrödinger operators with locally integrable potentials on infinite metric graphs, Applicable Analysis, 96:12, 2149-2161, DOI: 10.1080/00036811.2016.1207247, (2017).
