Coupled nonlinear Schroedinger equations for Langmuir and electromagnetic waves and extension of their modulational instability domain

A pair of coupled nonlinear Schroedinger equations for transverse and longitudinal waves are derived. The coupling resulting from equalization of group velocities drives the Langmuir waves modulationally unstable for wavelengths shorter than (msub(i)/msub(e))sup(1/2)lambdasub(D) and also extends the domain of modulational instability of electromagnetic waves when relativistic effects are taken into account. Instability is found to occur also for the perturbation wavenumber domain in which both the uncoupled Langmuir and electromagnetic waves are modulationally stable. Depending on the relative values of the self-modulation and coupling coefficients, the Langmuir or the transverse or both the waves may be localized in space. (author)