on-acoustic solitary waves in a weakly relativistic warm plasma at the critical phase
velocity are investigated using reductive perturbation theory. The basic set of fluid equations
describing the system is reduced to a renormalized warmion modified Korteweg—de Vries
(mKdV) equation for the first-order perturbed potential and a renormalized linear
inhomogeneous equation for the second-order perturbed potential. The stationary solution
of the coupled equations is obtained. The cold-plasma limit is considered in order to rule