  Rigorous pointwise asymptotics are established for semiclassical soliton
ensembles (SSEs) of the focusing nonlinear Schroedinger equation using
techniques of asymptotic analysis of matrix Riemann-Hilbert problems. The
accumulation of poles in the eigenfunction is handled using a new method in
which the residues are simultaneously interpolated at the poles by two distinct
interpolants. The results justify the WKB approximation for the nonselfadjoint
Zakharov-Shabat operator with real-analytic, bell-shaped, even potentials. The
new technique introduced in this paper is applicable to other problems as well:
(i) it can be used to provide a unified treatment by Riemann-Hilbert methods of
the zero-dispersion limit of the Korteweg-de Vries equation with negative
(soliton generating) initial data as studied by Lax, Levermore, and Venakides,
and (ii) it allows one to compute rigorous strong asymptotics for systems of
discrete orthogonal polynomials.
