Approximating tau-functions by theta-functions

2018/07/09 by Boris Dubrovin, Dubrovin, Boris · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AG #math.MP

paper · pdf · doi:10.48550/arxiv.1807.03377

14 pages, 2 figures

arxiv created 2018/07/09 · arxiv updated 2018/07/11

Abstract

We prove that the logarithm of an arbitrary tau-function of the KdV hierarchy can be approximated, in the topology of graded formal series by the logarithmic expansions of hyperelliptic theta-functions of finite genus, up to at most quadratic terms. As an example we consider theta-functional approximations of the Witten--Kontsevich tau-function.

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• On algebro-geometric solutions to the Gelfand--Dickey hierarchy

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