Resumen
The aim of this lecture is to provide novel results in the mathematical studies associated to the existence and orbital stability of standing wave solutions for the cubic nonlinear Schrödinger equation (NLS) on a looping edge graph GN, namely, a graph consisting of a circle and a finite amount N of infinite half-lines attached to a common vertex. By considering interactions of δ´-type (where continuity of the profiles at the vertex is not required), we study the dynamics of standing wave solutions with a periodic-profile on the circle and a family of soliton tail-profileson the half-lines. The existence and (in)stability of these profiles will depend on the relative size of the phase-velocity. The theory developed in this investigation has prospects for the study of other standing wave profiles of the NLS on a looping edge graph. This work was done incollaboration with Alexander Muñoz/IME-USP.
Ponente
Dr. Jaime Angulo Pava
Instituto de Matemática, Estatística e Ciência da Computação Universidade de São Paulo
Informes
luis.lopez@mym.iimas.unam.mx
daniel.castanon@iimas.unam.mx