This article presents a numerical and theoretical study of the
generation and propagation of oscillation in the semiclassical limit
ħ → 0 of the nonlinear paraxial equation. In a general
setting of both dimension and nonlinearity, the essential differences
between the “defocusing” and “focusing” cases
are observed. Numerical comparisons of the oscillations are made
between the linear (“free”) and the cubic (defocusing and
focusing) cases in one dimension. The integrability of the
one-dimensional cubic nonlinear paraxial equation is exploited to give
a complete global characterization of the weak limits of the
oscillations in the defocusing case.