| ABSTRACT: We will review recent results on the so-called semiclassical analysis of the integrable nonlinear Schroedinger equation in 1 + 1 dimensions. We will discuss the connection with an Euler hydrodynamic system and, more generally, the so-called Whitham equations. We will also make the connection with a variational problem of electrostatic type, under non-zero external field. Analytical tools used for proofs involve the theory of integrable equations and in particular Riemann-Hilbert factorization problems. |