18/09/2020 Colóquio (WEBINAR) Solitons and their interactions - Azadeh Mohammadi (Departamento de Física-UFPE)
Solitons and their interactions
Azadeh Mohammadi (Departamento de Física-UFPE)
In this talk, besides introducing the concept of the soliton and giving some historical context, I present a toy model we designed in 1+1 dimensions with kink solutions. The stability equation in the model is analogous to the Schrödinger equation with square-well potential. We modified the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasi-normal modes. I will refer to the kink excitations as well as kink-antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasi-normal modes. Besides that, I present a class of \phi^4n models with kink solutions where both tails of the kinks are long-range using a recently developed method of an accelerated kink ansatz to estimate the force between the kink and the antikink. The correct methods to study the collision of the kinks with long-range tails have been appearing recently invalidating many previous results reported in the literature.