  Propagation of a Brillouin precursor in a Lorentz dispersive medium is
considered. The precursor is excited by a sine modulated initial signal, with
its envelope described by a hyperbolic tangent function. The purpose of the
paper is to show how the rate of growth of the initial signal affects the form
of the Brillouin precursor. Uniform asymptotic approach, pertinent to
coalescing saddle points, is applied in the analysis. The results are
illustrated with numerical examples.
