  The propagation of ion acoustic shocks in nonthermal plasmas is investigated,
both analytically and numerically. An unmagnetized collisionless electron-ion
plasma is considered, featuring a superthermal (non-Maxwellian) electron
distribution, which is modeled by a $\kappa$- (kappa) distribution function.
Adopting a multiscale approach, it is shown that the dynamics of low-amplitude
shocks is modeled by a hybrid Korteweg-de Vries -- Burgers (KdVB) equation, in
which the nonlinear and dispersion coefficients are functions of the $\kappa$
parameter, while the dissipative coefficient is a linear function of the ion
viscosity. All relevant shock parameters are shown to depend on $\kappa$:
higher deviations from a pure Maxwellian behavior induce shocks which are
narrower, faster and of larger amplitude. The stability profile of the
kink-shaped solutions of the KdVB equation against external perturbations is
investigated and the spatial profile of the shocks is found to depend upon and
the role of the interplay between dispersion and dissipation is elucidated.
