Complex WKB method for calculating the asymptotic behavior of phase integrals

The complex variant of the WKB method developed in [1] when applied to an equation of Schrödinger type with constant coefficients gives one the possibility of calculating the asymptotic behavior of phase integrals with complex phase in the many-dimensional case. The resulting expressions are more convenient and apply in a more general situation than the expressions of the method of steepest descent.