Eduard-Wilhelm Kirr
University of Illinois at Urbana-Champaign, USA

I will present a new mathematical technique aimed at discovering all coherent structures supported by a given nonlinear wave equation. It relies on global bifurcation analysis which shows that, inside the Fredholm domain, the coherent structures organize themselves in in manifolds which either form closed surfaces or must reach the boundary of this domain. I will show how one can find all the limit points at the Fredholm boundary for the particular case of Nonlinear Schrödinger/Gross-Pitaevskii Equation and use these limit points to find all coherent structures and their bifurcation points.