Nonlinear Steepening of the Electrostatic Ion Cyclotron Wave

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Abstract
Electrostatic ion cyclotron waves observed in space at altitudes between 5000 and 8000 km often have a sinusoidal form. Occasionally, however, wave forms having a spiky or sawtooth form indicative of steepening are observed. The nonlinear fluid equations which characterize the electrostatic ion cyclotron wave have traveling-wave solutions with sinusoidal, spiky, and sawtooth forms. The wave form depends on the amplitude and phase velocity of the wave.