München 1997 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 8: Endliche Quantensysteme

MP 8.4: Fachvortrag

Thursday, March 20, 1997, 15:00–15:20, HS 110

On the inverse spectral method via Riemann-Hilbert problems — •T. Kriecherbauer¹, P. Deift², S. Kamvissis³, and X. Zhou⁴ — ¹Mathematisches Institut der Universität München, Theresienstr. 39, D-80333 München — ²Courant Institute, New York, USA — ³University of Marseille, France — ⁴Duke University, Durham, USA

About 25 years ago Shabat introduced a new formulation of the inverse spectral problem, i.e. to determine an operator from its scattering data, as a Riemann-Hilbert problem. This lead to new techniques for obtaining quantitative information on the underlying operator, which have been successfully employed to determine the long-time behavior of completely integrable systems such as Nonlinear Schroedinger equation, Korteweg-de Vries equation or Toda lattice. In this talk a concrete example (Toda lattice) will be used to demonstrate this method and discuss its applications.