Self-interaction of the upper hybrid wave

The self-interaction of the extraordinary mode propagating across the magnetostatic field in an electron plasma is investigated with particular attention to the range of frequencies close to the upper hybrid resonant frequency. The slowly varying amplitude of the upper hybrid wave satisfies a cubic Schrodinger equation which is deduced using the method of Kakutani and Sugimoto. The analysis of the Schrodinger equation shows that the extraordinary mode, in the neighborhood of the upper hybrid resonant frequency, is modulationally stable or unstable according to whether the wave number is below or above a critical value which is controlled only by the dispersive properties of the wave and which corresponds to frequencies slightly below the upper hybrid resonant frequency