Andres Gerardo Perez Yepez

Universidade de São Paulo

Title: Existence and orbital stability of standing wave solutions for the NLS-log equation on a tadpole graph.

Abstract: This poster aims to present a study of dynamic aspects of the nonlinear logarithmic Schrödinger equation (NLS-log) on a tadpole graph, that is, a graph composed of a circle with a half-line connected at a single vertex. By considering Neumann-Kirchhoff boundary conditions at the junction, the problems of existence and orbital stability of standing wave solutions with a profile determined by a positive single-lobe state are treated. Through an eigenvalue splitting method, we identify the Morse index and the null index of a specific linearized operator around a positive single-lobe state, which is essential in the study of stability.