The initial value problem, scattering and inverse scattering, for Schrödinger equations with a potential and a non-local nonlinearity
Year: 2006
Type: article
Abstract: We consider nonlinear Schrödinger equations with a potential, and non-local nonlinearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that are also models of molecular structure. We study in detail the initial value problem for these equations, in particular, existence and uniqueness of local and global solutions, continuous dependence on the initial data and regularity. We allow for a large class of unbounded potentials. We have no restriction on the growth at infinity of the positive part of the potential. We also construct the scattering operator in the case of potentials that go to zero at infinity. Furthermore, we give a method for the unique reconstruction of the potential from the small amplitude limit of the scattering operator. In the case of the quantum capacitor, our method allows us to uniquely reconstruct all the physical parameters from the small amplitude limit of the scattering operator.
Authors: María de los Ángeles Sand Romero, Ricardo Weder
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Award: G6683568797
OpenAlex ID: W1997907235