Nonlinear Stationary Phase

Spyros Kamvissis (University of Crete)

Tuesday 17th September, 2013 15:00-16:00 Maths 416


We consider the stability of the stationary and the periodic  Toda lattice under a "short range" perturbation. It is an old result  that in the first case the perturbed lattice asymptotically reduces to a finite system of solitons. In the periodic case, however it approaches a modulated lattice (plus a finite system of solitons) that we describe explicitly. Our method relies on the equivalence of the inverse spectral problem to a matrix Riemann-Hilbert factorisation problem: in the first case it is defined in the complex sphere while in the periodic case it  is defined in a hyperelliptic curve. We prove our result by applying (and generalising) the so-called nonlinear stationary phase method for Riemann-Hilbert problems.

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