Bethe Ansatz equations for the classical $A_n^{(1)}$ affine Toda field   theories
  We establish a correspondence between classical $A_n^{(1)}$ affine Toda field theories and $A_n$ Bethe Ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy functional relations of the type that appear in the context of the massive quantum integrable model. 
Panagiota Adamopoulou and Clare Dunning
math-ph math.MP