Small amplitude solitons in a warm plasma with smaller and higher order relativistic effects

Solitons have been investigated in a warm plasma through the Korteweg-de Vries (KdV) equation, considering a smaller relativistic effect for gamma approximate to O(v(2)/c(2)) and gamma(e)approximate to O(u(2)/c(2)) and higher relativistic effects for gamma approximate to O(v(4)/c(4)) and gamma(e)approximate to O(u(4/)c(4)). Compressive fast ion-acoustic solitons are observed to exist in the entire range (u(0)-v(0)) subject to a suitable mathematical condition satisfied by the initial streaming velocities u(0),v(0) of the electrons and the ions, respectively, electron to ion mass ratio Q(=m(e)/m(i)) and ion to electron temperature ratio sigma(=T-i/T-e). Further, rarefactive solitons of pretty small amplitudes are observed in the small upper range of vertical bar u(0)-v(0)vertical bar for higher order relativistic effect which are found to change parabolically. It is essentially important to report in our model of plasma, that the higher order relativistic effect slows down the soliton speed to V <= 0.10 for all temperature ratios sigma for small amplitude waves. On the other hand, the smaller order relativistic effect permits the soliton to exist even at a relatively much higher speed V < 0.30. Solitons of high (negligible) amplitudes are found to generate at the smaller (greater) difference of initial streamings (u(0)-v(0)) corresponding to both the relativistic effects. (c) 2007 American Institute of Physics.