Joint BCAM-UPV/EHU Analysis and PDE seminar: Local existence and scattering for models with internal structure

LOCATION: UPV/EHU room to be announced

Abstract
In this talk we will consider the nonlinear matrix Schrödinger equation on the half-line with general self-adjoint boundary condition. This model corresponds to a star graph describing the behavior of n connected very thin quantum wires that form a graph with only one vertex and a finite number of edges of infinite length. We will discuss the existence of local solutions for this model in the energy space. Moreover, we consider the scattering problem for this model. Under certain assumptions on the input data, we construct the wave, inverse wave and scattering operators. In particular, thanks to the general boundary conditions, we are able to obtain a scattering result for the nonlinear matrix Schrödinger equation on the line with a potential and point interactions

More info at https://sites.google.com/view/apdebilbao/home