Differential equation for a correlation function of the spin-${1\over2}$   Heisenberg chain
  We consider the probability to find a string of $x$ adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This system is completely integrable, it has Lax representation and a corresponding Riemann-Hilbert problem. The quantum correlation funtion is a $\tau$-function of this system. 
Holger Frahm, Alexander R. Its and Vladimir E. Korepin