Long time asymptotics of the finite Toda lattice

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Kyle Pounder
University of Arizona
Mon, 01/08/2018 - 4:00pm - 5:00pm
RH 306

The finite Toda lattice was proposed originally as a model for finitely many particles in a one-dimensional crystal. Now 50 years since its introduction, it has become a canonical model in integrable systems. In this talk, we will consider the long time limit of the finite Toda lattice. The main results are detailed asymptotic formulas for the positions and velocities of the particles, which improve upon classical results (Moser, 1975) by giving precise estimates of the associated error. Moreover, our Riemann-Hilbert techniques allow one, in principle, to compute the complete asymptotic expansions for the various dynamical quantities. This is joint work with Ken McLaughlin (Colorado State) and Bob Jenkins (University of Arizona).