Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations

Understand

The massive ODE/IM correspondence is a relation between the linear problem associated with modified affine Toda field equations and two-dimensional massive integrable models.

• We study the massive ODE/IM correspondence for the $A_r^{(1)}$-type modified affine Toda field equations.
• Based on the $\psi$-system satisfied by the solutions of the linear problem, we derive the Bethe ansatz equations and determine the asymptotic behavior of the Q-functions for large value of the spectral parameter.
• We derive the non-linear integral equations for the Q-functions from the Bethe ansatz equations.