On the numerical verification of a kernel assumption for the semi-relativistic Hartree equation
Abstract:
We consider the semi-relativistic Hartree equation with an external
potential. Recently this equation has been used to describe the dynamics
of boson stars under the influence of an external gravitational field.
This analysis makes one explicit critical assumption: Connected to the
dynamics problem there is an associated energy functional and the
assumption is on the size (number of elements) of the kernel of the
Hessian of this energy around a solitary wave. In this talk we give
indicators to that the assumption is valid. This is related to broken
symmetries of the associated energy functional.