### 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