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Fredholm determinants and the mKdV/sinh-Gordon hierarchies

Craig A. Tracy·Harold Widom
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Abstract

For a particular class of integral operators $K$ we show that the quantity \[\ph:=\log \det (I+K)-\log \det (I-K)\] satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

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Craig A. Tracy, Harold Widom. 1995-07-07. Fredholm determinants and the mKdV/sinh-Gordon hierarchies. https://doi.org/10.1007/bf02103713

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