Conserved energies for the one-dimensional cubic nonlinear defocusing Schrödinger equation with nonzero boundary conditions at infinity

Seminario de Ecuaciones

Speaker: Prof. Xian Liao

Abstract: In this talk we are going to construct a family of conserved energies for the one-dimensional cubic nonlinear defocusing Schrödinger equation, but with nonzero boundary conditions at infinity. This system is completely integrable by means of inverse scattering methods and admits Lax pair. We will introduce the associated energy spaces, and define the renormalized momentum as well as the renormalized transmission coefficient (associated to the Lax operator) on them. The conserved energies will be constructed in terms of this time-invariant transmission coefficient. This is joint work with Herbert Koch (Bonn, Germany)