Abstract:
One of the basic models for describing the generation of rogue waves due to
modulation instability is the focusing Nonlinear Schrodinger equation with
special Cauchy data; namely at the starting time one has a small perturbation
of the unstable background. In the spatially-periodic setting the spectral
curves corresponding to such initial data are small perturbations of the
rational ones, and very simple explicit formulas can be obtained. For small
number of unstable modes these formulas demonstrate a good agreement with the
results of numerical simulations. The talk is based on the joint work with
P. M. Santini.
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