  This paper is the first in a series devoted to the numerical study of
nonlinear interactions of electromagnetic waves with plasma. We start with
non-magnetized pair plasmas, where the primary processes are induced (Compton)
scattering and the filamentation instability. In this paper, we consider waves
in which electron oscillations are non-relativistic. Here, the numerical
results can be compared to analytical theory, facilitating the development of
appropriate numerical tools and framework. We distill the analytic theory,
reconciling plasma and radiative transfer pictures of induced scattering and
developing in detail the kinetic theory of modulation/filamentation
instability. We carry out homogeneous numerical simulations using the
particle-in-cell codes EPOCH and Tristan-MP, for both monochromatic waves and
wave packets. We show that simulations of both processes are consistent with
theoretical predictions, setting the stage for analyzing the highly nonlinear
regime.
