  Compressional waves propagating in the partially ionised solar lower
atmospheric plasmas can easily steepen into nonlinear waves, including shocks.
Here we investigate the effect of weak dispersion generated by Hall currents
perpendicular to the ambient magnetic field on the characteristics of shock
waves. Our study will also focus on the interplay between weak dispersion and
partial ionisation of the plasma. Using a multiple scale technique we derive
the governing equation in the form of a Korteweg-de Vries-Burgers equation. The
effect of weak dispersion on shock waves is obtained using a perturbation
technique. The secular behaviour of second order terms is addressed with the
help of a renormalisation technique. Our results show that dispersion modifies
the characteristics of shock waves and this change is dependent also on the
ionisation degree of the plasma. Dispersion can create short lived oscillations
in the shocked plasma. The shock fronts become wider with the increase in the
number of neutrals in the plasma.
