### Abstract

procedure is illustrated by considering a number of examples.

Language | English |
---|---|

Pages | 593-613 |

Number of pages | 21 |

Journal | Progress of Theoretical Physics |

Volume | 127 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2012 |

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### Keywords

- inverse scattering
- Vakhnenko-Parkes equation
- discrete spectrum
- continuous spectrum

### Cite this

*Progress of Theoretical Physics*,

*127*(4), 593-613. https://doi.org/10.1143/PTP.127.593

}

*Progress of Theoretical Physics*, vol. 127, no. 4, pp. 593-613. https://doi.org/10.1143/PTP.127.593

**Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation.** / Vakhnenko, V.O.; Parkes, E.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation

AU - Vakhnenko, V.O.

AU - Parkes, E.J.

PY - 2012/4

Y1 - 2012/4

N2 - In this paper the inverse scattering method is applied to the Vakhnenko-Parkes equation. We describe a procedure for using the inverse scattering transform to find the solutions that are associated with both the bound state spectrum and continuous spectrum of the spectral problem. The suggested special form of the singularity function gives rise to the multi-mode periodic solutions. Sufficient conditions are obtained in order that the solutions become real functions. The interaction of the solitons and multi-mode periodic waves is studied. Theprocedure is illustrated by considering a number of examples.

AB - In this paper the inverse scattering method is applied to the Vakhnenko-Parkes equation. We describe a procedure for using the inverse scattering transform to find the solutions that are associated with both the bound state spectrum and continuous spectrum of the spectral problem. The suggested special form of the singularity function gives rise to the multi-mode periodic solutions. Sufficient conditions are obtained in order that the solutions become real functions. The interaction of the solitons and multi-mode periodic waves is studied. Theprocedure is illustrated by considering a number of examples.

KW - inverse scattering

KW - Vakhnenko-Parkes equation

KW - discrete spectrum

KW - continuous spectrum

UR - http://ptp.ipap.jp/link?PTP/127/593/

U2 - 10.1143/PTP.127.593

DO - 10.1143/PTP.127.593

M3 - Article

VL - 127

SP - 593

EP - 613

JO - Progress of Theoretical Physics

T2 - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 4

ER -