Beam propagation in a nonlinear Kerr medium is considered within a frame of first-order nonlinear optics. An optical signal of cylindrical symmetry is described by its variance matrix of second-order moments. The beam propagation through the nonlinear sample is traced by a nonlinearly modified ray transfer matrix. The Wigner distribution function in a novel semi-linear analytic form is defined by use of booth these matrices in a scaled phase space. Numerical data pertaining to beam tracing at a self-trapping power level are given for initially chirped signals and for propagation distances that include self-collapse points.
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