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