### Abstract

We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, where τ_{0} ≤ 1. The τ-functions τ_{n} are given by the Pfaffians of a certain skew-symmetric matrix. We identify a one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by a 4N × 4N skew-symmetric constant matrix which we call the B-matrix. We then find that one can have M-soliton solutions with M being any number from N to 2N - 1 for some of the 4N × 4N B-matrices having only 2N nonzero entries in the upper-triangular part (the number of solitons obtained from those B-matrices was previously expected to be just N).

Original language | English |
---|---|

Pages (from-to) | 4063-4086 |

Number of pages | 24 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2006 Apr 14 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*39*(15), 4063-4086. https://doi.org/10.1088/0305-4470/39/15/012

**N-soliton solutions to the DKP equation and Weyl group actions.** / Kodama, Yuji; Maruno, Kenichi.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 39, no. 15, pp. 4063-4086. https://doi.org/10.1088/0305-4470/39/15/012

}

TY - JOUR

T1 - N-soliton solutions to the DKP equation and Weyl group actions

AU - Kodama, Yuji

AU - Maruno, Kenichi

PY - 2006/4/14

Y1 - 2006/4/14

N2 - We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, where τ0 ≤ 1. The τ-functions τn are given by the Pfaffians of a certain skew-symmetric matrix. We identify a one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by a 4N × 4N skew-symmetric constant matrix which we call the B-matrix. We then find that one can have M-soliton solutions with M being any number from N to 2N - 1 for some of the 4N × 4N B-matrices having only 2N nonzero entries in the upper-triangular part (the number of solitons obtained from those B-matrices was previously expected to be just N).

AB - We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, where τ0 ≤ 1. The τ-functions τn are given by the Pfaffians of a certain skew-symmetric matrix. We identify a one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by a 4N × 4N skew-symmetric constant matrix which we call the B-matrix. We then find that one can have M-soliton solutions with M being any number from N to 2N - 1 for some of the 4N × 4N B-matrices having only 2N nonzero entries in the upper-triangular part (the number of solitons obtained from those B-matrices was previously expected to be just N).

UR - http://www.scopus.com/inward/record.url?scp=33645518684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645518684&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/15/012

DO - 10.1088/0305-4470/39/15/012

M3 - Article

AN - SCOPUS:33645518684

VL - 39

SP - 4063

EP - 4086

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 15

ER -