The discrete potential Boussinesq equation and its multisoliton solutions

Ken Ichi Maruno; Kenji Kajiwara

doi:10.1080/00036810903569473

The discrete potential Boussinesq equation and its multisoliton solutions

Ken Ichi Maruno, Kenji Kajiwara

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	593-609
Number of pages	17
Journal	Applicable Analysis
Volume	89
Issue number	4
DOIs	https://doi.org/10.1080/00036810903569473
Publication status	Published - 2010 Apr
Externally published	Yes

Keywords

Bilinear equations
Discrete potential Boussinesq equation
Multisoliton solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/00036810903569473

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title = "The discrete potential Boussinesq equation and its multisoliton solutions",

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.",

keywords = "Bilinear equations, Discrete potential Boussinesq equation, Multisoliton solutions",

author = "Maruno, {Ken Ichi} and Kenji Kajiwara",

note = "Funding Information: 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.",

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AU - Maruno, Ken Ichi

AU - Kajiwara, Kenji

N1 - Funding Information: 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.

PY - 2010/4

Y1 - 2010/4

N2 - 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.

AB - 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.

KW - Bilinear equations

KW - Discrete potential Boussinesq equation

KW - Multisoliton solutions

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The discrete potential Boussinesq equation and its multisoliton solutions

Abstract

Keywords

ASJC Scopus subject areas

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