ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation

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We study the massive ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation.

• Based on the $\psi$-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations.
• We also discuss the T-Q relations, the T-system and the Y-system, which are shown to be related to those of the $A_3/{\bf Z}_2$ integrable system.
• We consider the case that the solution of the linear problem has a monodromy around the origin, which imposes nontrivial boundary conditions for the T-/Y-system.