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SMC Colloquium

Analytic and combinatorial aspects of the Non Linear Schroedinger equation (NLS) on a torus

by Claudio Procesi (Univ. di Roma, La Sapienza)

Lecture hall Oskar Klein ()

Lecture hall Oskar Klein


The approach to the NLS on a torus is usually by perturbation theory starting from solutions involving some finite set of “excited frequencies”. These form a finite set of points in a lattice which generate a complicated combinatorial graph describing interacting frequencies.

The behaviour of the solutions depends on the combinatorics of this graph which in turn depends on the chosen initial points, for generic choices one has quasi periodic solutions for special choices different types of behaviour.