ODE/IM correspondence for affine Lie algebras: A numerical approach

Understand

We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type.

• We consider the linear problem obtained from the massless limit of that of the modified affine Toda field equation.
• We found that the Q-functions in integrable models are expressed as the inner product of the solution of the dual linear problem and the subdominant solution of the linear problem.
• Using Cheng's algorithm to obtain the solution of the linear problem, we can determine efficiently the zeros of the Q-function, which is known to provide the solutions of the Bethe ansatz equations.