The interaction among non-resonant ion acoustic plasma waves with
different
group velocities that are not close to each other is studied by an asymptotic
perturbation method, based on Fourier expansion and spatio-temporal
rescaling. It is shown that the nonlinear Schrödinger equation is
not adequate,
and instead a model system of nonlinear evolution equations is necessary
to
describe oscillation amplitudes of Fourier modes. This system is C-integrable,
i.e. it can be linearized through an appropriate transformation of the
dependent
and independent variables. We demonstrate that the subclass of localized
solutions gives rise to a solitonic phenomenology. These solutions propagate
with the relative group velocity and maintain their shape during a collision,
the
only change being a phase shift. Numerical calculations confirm the validity
of
these predictions.