  In this paper we examine the semiclassical behaviour of the scattering data
of a non-self-adjoint Dirac operator with analytic potential decaying at
infinity. In particular, employing the exact WKB method, we provide the
complete rigorous uniform semiclassical analysis of the reflection coefficient
and the Bohr-Sommerfeld condition for the location of the eigenvalues. Our
analysis has some interesting consequences concerning the focusing cubic NLS
equation, in view of the well-known fact discovered by Zakharov and Shabat that
the spectral analysis of the Dirac operator is the basis of the solution of the
NLS equation via inverse scattering theory.
