  By considering the continuity, Navier-Stoks and Poisson's equations in a
non-relativistic frame work for plasmas, we study the behavior of small
amplitude ion acoustic solitary waves in plasmas under the influence of a
varying magnetic field. The result is a nonlinear wave equation which complies
with the KdV-Burgers (KdVB) equation, surprisingly in the absence of thermal
pressure or any dissipative effects. We show that the complete set of
equations, by considering the varying magnetic field, create solitary waves
which radiate energy during their traveling in the medium. An interesting
result is the existence of small amplitude localized shock profiles beside the
solitary waves. Properties of this solitaire solution is studied by considering
different values for the environmental characters.
