  An alternate form of discrete potential Boussinesq equation is proposed and
its multisoliton solutions are constructed. An ultradiscrete potential
Boussinesq equation is also obtained from the discrete potential Boussinesq
equation using the ultradiscretization technique. The detail of the
multisoliton solutions is discussed by using the reduction technique. The
lattice potential Boussinesq equation derived by Nijhoff et al. is also
investigated by using the singularity confinement test. The relation between
the proposed alternate discrete potential Boussinesq equation and the lattice
potential Boussinesq equation by Nijhoff et al. is clarified.
