Functional relations in Stokes multipliers - Fun with $x^6 + \alpha x^2$ potential-

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x^6 + \alpha x^2, for example . The space coordinate is continued to a complex plane and the connection problem of fundamental system of solutions is considered. A hidden U_q(\hat{gl}(2|1)) structure arises in "fusion relations" of Stokes multipliers. With this observation, we derive coupled nonlinear integral equations which characterize the spectral properties of both \pm \alpha potentials simultaneously. equations.