El Coloquio IIMAS surge con el objetivo de tener mayor interacción entre los grupos de investigación en Matemáticas Aplicadas, Ciencia e Ingeniería de la Computación y los Sistemas.
Con ello, el Coloquio IIMAS busca enriquecer los conocimientos universales en las áreas de investigación de este Instituto, fomentando la creación de grupos multidisciplinarios, el desarrollo tecnológico e innovador y la difusión del conocimiento.
Las temáticas del Coloquio IIMAS cambiarán cada semestre buscando cubrir todas las áreas de investigación del Instituto.
Resumen
This talk concerns the (generalized) Soler model: a nonlinear (massive) Dirac equation with a nonlinearity taking the form of a space-dependent mass. The equation admits standing wave solutions and they are generally expected to be stable (i.e., small perturbations in the initial conditions stay small) based on numerical simulations. However, contrarily to the nonlinear Schrödinger equation for example, there are very few results in this direction. The results that I will discuss concern the simpler question of spectral stability (and instability), i.e., the absence (or presence) of exponentially growing solutions to the linearized equation around a solitary wave. As in the case of the nonlinear Schrödinger equation, this is equivalent to the presence or absence of “unstable eigenvalues” of a non selfadjoint operator with a particular block structure. I will highlight the differences and similarities with the Schrödinger case, present results for the one-dimensional case, and discuss open problems. This is joint work with Danko Aldunate, Edgardo Stockmeyer, and Hanne Van Den Bosch.
Ponente
Dr. Julien M. Ricaud
Departamento de Física y Matemáticas, IIMAS, UNAM
https://www.iimas.unam.mx/ricaud/index_EN.php
Informes
coloquio@iimas.unam.mx
Comité organizador
Pablo Barberis Blostein
pbb@iimas.unam.mx
Diego Alejandro Iniesta Miranda
diegoinesta@ciencias.unam.mx
J. Roberto Romero Arias
romero@mym.iimas.unam.mx