A non-linear differential equation and a Fredholm determinant

M. Mehta

In several branches of mathematical physics one comes across the Fredholm determinant of the kernel sin (x-y)π/(x-y)π on the finite interval (-t,t). Jimbo, Miwa, Mori and Sato derived a non-linear differential equation for it. We reinvestigate this problem, find five equations satisfied by three functions A(t), B(t) and S(t) related to this Fredholm determinant, and as a consequence deduce the differential equation of Jimbo, Miwa, Mori and Sato.

Domaines: Articles anciens

M. Mehta. A non-linear differential equation and a Fredholm determinant. Journal de Physique I, 1992, 2 (9), pp.1721-1729. ⟨10.1051/jp1:1992240⟩. ⟨jpa-00246654⟩