### Abstract

The reciprocal link between the reduced Ostrovsky equation and the A ^{(2)} _{2} two-dimensional Toda (2D-Toda) system is used to construct the N-soliton solution of the reduced Ostrovsky equation. The N-soliton solution of the reduced Ostrovsky equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations and the τ-function of the reduced Ostrovsky equation are obtained from the period 3-reduction of the B or C 2D-Toda system, i.e. the A ^{(2)} _{2} 2D-Toda system. One of the τ-functions of the A ^{(2)} _{2} 2D-Toda system becomes the square of a pfaffian which also becomes a solution of the reduced Ostrovsky equation. There is another bilinear equation which is a member of the 3-reduced extended BKP hierarchy. Using this bilinear equation, we can also construct the same pfaffian solution.

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

Article number | 355203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 45 |

Issue number | 35 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

^{(2)}

_{2}two-dimensional Toda system.

*Journal of Physics A: Mathematical and Theoretical*,

*45*(35), [355203]. https://doi.org/10.1088/1751-8113/45/35/355203

**On the τ-functions of the reduced Ostrovsky equation and the A ^{(2)} _{2} two-dimensional Toda system.** / Feng, Bao Feng; Maruno, Kenichi; Ohta, Yasuhiro.

Research output: Contribution to journal › Article

^{(2)}

_{2}two-dimensional Toda system',

*Journal of Physics A: Mathematical and Theoretical*, vol. 45, no. 35, 355203. https://doi.org/10.1088/1751-8113/45/35/355203

}

TY - JOUR

T1 - On the τ-functions of the reduced Ostrovsky equation and the A (2) 2 two-dimensional Toda system

AU - Feng, Bao Feng

AU - Maruno, Kenichi

AU - Ohta, Yasuhiro

PY - 2012

Y1 - 2012

N2 - The reciprocal link between the reduced Ostrovsky equation and the A (2) 2 two-dimensional Toda (2D-Toda) system is used to construct the N-soliton solution of the reduced Ostrovsky equation. The N-soliton solution of the reduced Ostrovsky equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations and the τ-function of the reduced Ostrovsky equation are obtained from the period 3-reduction of the B or C 2D-Toda system, i.e. the A (2) 2 2D-Toda system. One of the τ-functions of the A (2) 2 2D-Toda system becomes the square of a pfaffian which also becomes a solution of the reduced Ostrovsky equation. There is another bilinear equation which is a member of the 3-reduced extended BKP hierarchy. Using this bilinear equation, we can also construct the same pfaffian solution.

AB - The reciprocal link between the reduced Ostrovsky equation and the A (2) 2 two-dimensional Toda (2D-Toda) system is used to construct the N-soliton solution of the reduced Ostrovsky equation. The N-soliton solution of the reduced Ostrovsky equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations and the τ-function of the reduced Ostrovsky equation are obtained from the period 3-reduction of the B or C 2D-Toda system, i.e. the A (2) 2 2D-Toda system. One of the τ-functions of the A (2) 2 2D-Toda system becomes the square of a pfaffian which also becomes a solution of the reduced Ostrovsky equation. There is another bilinear equation which is a member of the 3-reduced extended BKP hierarchy. Using this bilinear equation, we can also construct the same pfaffian solution.

UR - http://www.scopus.com/inward/record.url?scp=84865218628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865218628&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/45/35/355203

DO - 10.1088/1751-8113/45/35/355203

M3 - Article

VL - 45

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 35

M1 - 355203

ER -