  We are interested in a WKB analysis of the Logarithmic Non-Linear
Schr\"odinger Equation with "Riemann-like" variables in an analytic framework
in semiclassical regime. We show that the Cauchy problem is locally well posed
uniformly in the semiclassical constant and that the semiclassical limit can be
performed. In particular, our framework is not only compatible with the
Gross-Pitaevskii equation with logarithmic nonlinearity, but also allows
initial data (and solutions) which can converge to $0$ at infinity.
