### Abstract

Ultradiscrete soliton equations and Bäcklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete Korteweg-de Vries (KdV) equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between Bäcklund transformations for discrete and ultradiscrete KdV equations.

Original language | English |
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Article number | 375202 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 37 |

DOIs | |

Publication status | Published - 2010 Sep 17 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

**Bilinear equations and Bäcklund transformation for a generalized ultradiscrete soliton solution.** / Nagai, Hidetomo; Takahashi, Daisuke.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Bilinear equations and Bäcklund transformation for a generalized ultradiscrete soliton solution

AU - Nagai, Hidetomo

AU - Takahashi, Daisuke

PY - 2010/9/17

Y1 - 2010/9/17

N2 - Ultradiscrete soliton equations and Bäcklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete Korteweg-de Vries (KdV) equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between Bäcklund transformations for discrete and ultradiscrete KdV equations.

AB - Ultradiscrete soliton equations and Bäcklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete Korteweg-de Vries (KdV) equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between Bäcklund transformations for discrete and ultradiscrete KdV equations.

UR - http://www.scopus.com/inward/record.url?scp=78649587326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649587326&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/43/37/375202

DO - 10.1088/1751-8113/43/37/375202

M3 - Article

AN - SCOPUS:78649587326

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 37

M1 - 375202

ER -