  The interaction between two co-propagating electrostatic wavepackets
characterized by arbitrary carrier wavenumber is considered. A one-dimensional
(1D) non-magnetized plasma model is adopted, consisting of a cold inertial ion
fluid evolving against a thermalized (Maxwell-Boltzmann distributed) electron
background. A multiple-scale perturbation method is employed to reduce the
original model equations to a pair of coupled nonlinear Schr\"odinger (CNLS)
equations governing the dynamics of the wavepacket amplitudes (envelopes). The
CNLS equations are in general asymmetric for arbitrary carrier wabvenumbers.
Similar CNLS systems have been derived in the past in various physical
contexts, and were found to support soliton, breather, and rogue wave
solutions, among others. A detailed stability analysis reveals that
modulational instability (MI) is possible in a wide range of values in the
parameter space. The instability window and the corresponding growth rate are
determined, considering different case studies, and their dependence on the
carrier and the perturbation wavenumber is investigated from first principles.
Wave-wave coupling is shown to favor MI occurrence by extending its range of
occurrence and by enhancing its growth rate. Our findings generalize previously
known results usually associated with symmetric NLS equations in nonlinear
optics, though taking into account the difference between the different
envelope wavenumbers and thus group velocities.
