Double layers, spiky solitary waves, and explosive modes of relativistic ion‐acoustic waves propagating in a plasma

The fully relativistic ion fluid equations are presented. These equations are reduced to a mixed modified Korteweg–de Vries (MKdV) equation by using the reductive perturbation method. The high‐speed streaming ions and the negative cubic nonlinearity of the mixed MKdV equation give rise to the new nonlinear wave modes, that is, the compressive double layer, the spiky solitary wave, and the explosive solutions. The double layer and the spiky solitary wave are confined within the specified positive potential region, while the explosive solutions are confined within the region where the potential exceeds the maximum potential or the negative potential region. It is shown for the first time that the double‐layer thickness narrows as the ion temperature and the relativistic effects increase, that the potential drop of the double layer grows as the ion temperature increases, and that the amplitudes of the spiky solitary wave and the explosive solution grow as the ion temperature effect increases. This investigation relates to the evolution process of the nonlinear wave structure in which these three modes form the fine structure in space.