A new model for the near-wake studies is presented. It pertains to a tenuous plasma medium with negligible magnetic field effects. The wake-generating body moves at a mesothermal speed (Vb) i.e. intermediate between the thermal speeds of ions and electrons of the ambient plasma which is bi-thermal (Tie) and has a Debye length (&lgr;D= (kTe/4&pgr;e2n0)1/2 much smaller than the body size. The model is constructed by using the concept that the cavity left by a rapidly moving body acts as a generator of finite-amplitude ion acoustic waves which are excited by an initial discontinuity of plasma density at the leading edge of the cavity. This ionic wave motion, represented by fluid equations, is represented approximately by the time dependent (t), one-dimensional (x) Korteweg-de Vries equation. The solution to the KdV equation in (x,t) variables is shown to be closely related to the stationary solution of a two-dimensional wake in [x,z(=Vbt)> variables relative to a frame fixed to the body. Numerical and analytic solutions are both given.