Title: Short-Time Nonlinear Effects in the Exciton-Polariton System,
Abstract: In the exciton-polariton system, a linear dispersive photon field is coupled
to a nonlinear exciton field. Short-time analysis of the lossless system shows
that, when the photon field is excited, the time required for that field to
exhibit nonlinear effects is longer than the time required for the nonlinear
Schrödinger equation, in which the photon field itself is nonlinear. When the
initial condition is scaled by $\epsilon^\alpha$, it is found that the relative
error committed by omitting the nonlinear term in the exciton-polariton system
remains within $\epsilon$ for all times up to $t=C\epsilon^\beta$, where
$\beta=(1-\alpha(p-1))/(p+2)$. This is in contrast to $\beta=1-\alpha(p-1)$ for
the nonlinear Schrödinger equation.