  Nonlinear Schr\"odinger equation (with the Schwarzian initial data) is
important in nonlinear optics, Bose condensation and in the theory of strongly
correlated electrons. The asymptotic solutions in the region $x/t={\cal O}(1)$,
$t\to\infty$, can be represented as a double series in $t^{-1}$ and $\ln t$.
Our current purpose is the description of the asymptotics of the coefficients
of the series.
