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The nonlinear coupling between two perpendicularly propagating (with respect to the external magnetic field direction) upper-hybrid (UH) waves in a uniform magnetoplasma is considered, taking into account quasi-stationary density perturbations which are driven by the UH wave ponderomotive force. This interaction is governed by a pair of coupled nonlinear Schrödinger equations (CNLSEs) for the UH wave envelopes. The CNLSEs are used to investigate the occurrence of modulational instability. Waves in the vicinity of the UH resonance are considered, so that the group dispersion terms for both waves are approximately equal, but the UH wave group velocities may be different. It is found that a pair of unstable UH waves (obeying anomalous group dispersion) yields an increased instability growth rate, while a pair of stable UH waves (individually obeying normal group dispersion) remains stable for equal group velocities, although it is destabilized by a finite group velocity mismatch. Stationary nonlinear solutions of the CNLSEs are presented.

Modulational instability and localized excitations involving two nonlinearly coupled upper-hybrid waves in plasmas