Resumen
The aim of this lecturer is to present new spectral tools for studying the orbital stability of standing wave solutions for the nonlinear Schrödinger equation (NLS) with power nonlinearity on a tadpole graph, a graph consisting of a ring and a half-line attached at a single vertex. By considering a δ-interaction type boundary condition at the junction of the graph, we study the stability properties of positive two-lobe state profiles for every positive power nonlinearity. Our arguments are based in a new splitting eigenvalue method for Schrödinger operators on a tadpole graph, as well as, in the extension theory of Krein & von Neumann for symmetric operators and in the oscillation theory for real coupled selfadjoint boundary conditions. As application of the period function for second-order differential equations and our study, we establish the existence and stability of positive two-lobe state of the cubic NLS. Our work extends to looping edge graphs, a graph consisting of a ring attached to many half-lines at one vertex.
Imparte
Dr. Jaime Angulo Pava
Institute of Mathematics and Statistics,
University of S.o Paulo
Registo previo
luis.lopez@aries.iimas.unam.mx
calleja@mym.iimas.unam.mx
Zoom: https://shorturl.at/Cv0GO