This problem is motivated by the long-time behaviour in solutions of nonlinear Schroedinger equations and essentially amounts to finding the solutions of an underdetermined system of linear equations subject to certain constraints which can be described geometrically and in terms of graph theory. This is a nice challenging problem that allows both analytical and computational approaches for its study.
It will involve a collaboration with Prof. Eduard Kirr at University of Illinois at Urbana-Champaign, USA
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