### Abstract

The Degasperis-Procesi (DP) equation is investigated from the point of view of determinant-Pfaffian identities. The reciprocal link between the DP equation and the pseudo 3-reduction of the C_{∞} two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of Pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and Pfaffians, and the τ-functions of the DP equation are obtained from the pseudo 3-reduction of the C_{∞} two-dimensional Toda system.

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

Article number | 045205 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Feb 1 |

Externally published | Yes |

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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

*Journal of Physics A: Mathematical and Theoretical*,

*46*(4), [045205]. https://doi.org/10.1088/1751-8113/46/4/045205

**On the τ-functions of the Degasperis-Procesi equation.** / Feng, Bao Feng; Maruno, Kenichi; Ohta, Yasuhiro.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 46, no. 4, 045205. https://doi.org/10.1088/1751-8113/46/4/045205

}

TY - JOUR

T1 - On the τ-functions of the Degasperis-Procesi equation

AU - Feng, Bao Feng

AU - Maruno, Kenichi

AU - Ohta, Yasuhiro

PY - 2013/2/1

Y1 - 2013/2/1

N2 - The Degasperis-Procesi (DP) equation is investigated from the point of view of determinant-Pfaffian identities. The reciprocal link between the DP equation and the pseudo 3-reduction of the C∞ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of Pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and Pfaffians, and the τ-functions of the DP equation are obtained from the pseudo 3-reduction of the C∞ two-dimensional Toda system.

AB - The Degasperis-Procesi (DP) equation is investigated from the point of view of determinant-Pfaffian identities. The reciprocal link between the DP equation and the pseudo 3-reduction of the C∞ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of Pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and Pfaffians, and the τ-functions of the DP equation are obtained from the pseudo 3-reduction of the C∞ two-dimensional Toda system.

UR - http://www.scopus.com/inward/record.url?scp=84872721530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872721530&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/4/045205

DO - 10.1088/1751-8113/46/4/045205

M3 - Article

AN - SCOPUS:84872721530

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 4

M1 - 045205

ER -