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Abstract
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.
Acknowledgements
The authors would like to thank Prof Masayuki Oikawa for stimulating discussions. The authors would like to acknowledge helpful comments and suggestions of the referees. The authors are grateful for the hospitality of the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge where this article was completed during the programme Discrete Integrable Systems (DIS). This work was partially supported by the JSPS Grant-in-Aid for Scientific Research No. 21656027 and No. 19340039.
