The effect of the ion temperature on large amplitude ion-acoustic waves is studied in an electron–positron–ion plasma. The region of the existence of the ion-acoustic waves is presented, by the analysis of the structure of the pseudopotential. It is found that the ion temperature increases the maximum Mach number and decreases the amplitude of the ion-acoustic waves. The region of the existence sensitively depends on the ion temperature and the positron density and temperature. It is shown that the region of the existence of the ion-acoustic wave spreads as the ion temperature decreases. The present theory is applicable to analyzing large amplitude ion-acoustic waves in an electron–positron–ion plasma associated with the ion temperature which may occur in space.

The effect of the ion temperature on ion acoustic solitary waves in a collisionless relativistic plasma is discussed using the Korteweg–de Vries equation. The phase velocity of the ion acoustic waves decreases as the relativistic effect increases, and increases as the ion temperature increases. Only a compressional soliton of the ion acoustic wave is formed in this system. Since its amplitude increases for the lower ion temperature as the relativistic effect increases, we deduce the formation of a precursor by the presence of the streaming ions. In contrast, for the higher ion temperature, the amplitude decreases slowly. Furthermore, it is shown that the oscillatory solution of the Korteweg–de Vries equation smoothly links with the nonlinear Schrödinger equation in a relativistic plasma.

The effect of the dust charging and the influence of the ion density and temperature on electrostatic nonlinear ion waves in a dusty plasma having trapped electrons are investigated by numerical calculation. The nonlinear structure of the dust charging is examined, and it is shown that the characteristics of the dust charge number sensitively depend on the electrostatic potential, Mach number, trapped electron temperature, ion density, and temperature. An increase of the ion temperature decreases the dust charging rate and the propagation speed of ion waves. It turns out that a decrease of the trapped electron temperature increases the charging rate of dust grains. It is found that the existence of ion waves sensitively depends on the ion to electron density ratio. New findings of variable-charge dust grain particles, ion density, and temperature in a dusty plasma with trapped electrons are predicted.

The nonlinear wave structures of large amplitude ion-acoustic waves are studied in a plasma with positrons. We have presented the region of existence of the ion-acoustic waves by analysing the structure of the pseudopotential. The region of existence sensitively depends on the positron to electron density ratio, the ion to electron mass ratio and the positron to electron temperature ratio. It is shown that the maximum Mach number increases as the positron temperature increases and the region of existence of the ion-acoustic waves spreads as the positron temperature increases. The present theory is applicable to analyse large amplitude ion-acoustic waves associated with positrons which may occur in space plasmas.

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.