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Whitham equations, Bergman kernel and logarithmic potential theory

Monday 15th October 2001 - 15:00 to 16:00
INI Seminar Room 1
We show that the Bergman kernel, defined on hyperelliptic Riemann surfaces, solves two different variational problems. First we show that it provides the solution of the Whitham equations for KdV and NLS. Then we show that the equilibrium measure for logarithmic potentials in the presence of an external field can be expressed in terms of the Bergman kernel.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons