A study of Korteweg de-Vries, modified Korteweg de-Vries and Kadomtsev-Petviashvili solitons in a multispecies collisionless weakly relativistic plasma

The effect on the propagation of ion acoustic solitons and double layers has been studied in collisionless weakly relativistic plasma consisting of two electron temperature with isothermal electrons and finite ion temperature. The Korteweg de-Vries (KdV) equation is derived for ion-acoustic solitons propagating in a collisionless plasma. This equation is solved in a stationary frame to obtain the expression for soliton phase velocity, soliton width, peak soliton amplitude and soliton energy. It is observed that these quantities are significantly influenced by relativistic effect, ion temperature, low temperature electron density and ratio of cold to hot electron temperature. Many features expected from hot ion theory and two species electron plasmas automatically emerge. The analysis is further extended to higher order nonlinearity and modified Korteweg de-Vries (mKdV) equation is derived. Under suitable approximation double-layer solution is obtained. It is found that only rarefactive double layers exist for certain range of low temperature electrons. Finally, the problem is extended to two dimensions and Kadomtsev-Petaviashili (K P) equation is derived.