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.