The Stokes multiplier for the Landau-Zener model

A new method is presented for calculating the Stokes multiplier for the Landau-Zener model. This method is based on the coupled wave integral equations suggested by Hinton. The calculations are reduced to the matching of the solution of the third-order recursion relation to the asymptotic Birkhoff set. An analytical application of the method is given for the perturbation theory limit at the energy equal to zero.