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A new amplitude equation governing the velocity evolution of ion-acoustic waves in a collisionless plasma is derived: Vtt+(V2)xt=(1−V2)Vx x+βVxxtt. From this equation the existence of a critical amplitude threshold is immediately deduced, which leads to a double layer and above which solitary waves cannot exist. Above this threshold shock waves form and density undergoes explosive growth. Multidimensional waves and waves due to the magnetic drift are also considered.
Philip Rosenau (Wed,) studied this question.
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