Dia: Dimecres, 21 de març de 2018
Lloc: Aula S01, Facultat de Matemàtiques i Estadística, UPC.
A càrrec de: Otávio Gomid, Universidade Estadual de Campinas i UPC
Títol: Critical Energy in Soliton-Defect Interaction Models
Resum: In this talk, we present a toy-model for interactions between kinks (solitons) of the sine-Gordon equation and a weak defect (a small perturbation modeled by a Dirac delta function). We consider a finite-dimensional reduction of the sine-Gordon equation which is given by a 2-degrees of freedom Hamiltonian H, and we propose a geometric approach to give conditions on the energy of the system to admit kinks. More precisely, we obtain an asymptotic expression of the critical energy hc for which the system admits kinks with small amplitude for energies h≥hc. Our methods rely on computing the exponentially small transversality of invariant manifolds Wu,s of certain objects (critical points and periodic orbits) at infinity.
This is a joint work with M. Guardia and T. M. Seara.
Last updated: Mon Mar 19 08:35:17 2018