Herbert Koch (Bonn)
A continuous family of conserved energies for the Gross-Pitaevskii equation
The Gross-Pitaevskii equation is the defocusing cubic nonlinear
Schrödinger equation with the boundary conditions |u(t,x)| -> 1
at infinity. A difficulty in the study of the Gross-Pitaevskii equation
is that the state space is nonlinear. In joint work with Xian Liao we
study the equation in one space dimension, equip it with a new metric,
and construct a continuous family of conserved energies.