Fredholm determinants and the mKdV/sinh-Gordon hierarchies
- Author(s): Tracy, Craig A.;
- Widom, Harold
- et al.
Published Web Locationhttps://arxiv.org/pdf/solv-int/9506006.pdf
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.