Functional relations in stokes multipliers -: Fun with x6+ax2 potential

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential tel ms, x(6) + alphax(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((gl) over cap (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 +/- alpha potentials simultaneously.