### Abstract

of the inverse scattering method is described. The continuous spectrum is taken into

account in the associated eigenvalue problem. The suggested special form of the

singularity function for continuous part of the spectral data gives rise to the multimode solutions. The sufficient conditions are proved in order that these solutions become real functions. The interaction of the N periodic waves is studied. The procedure is illustrated by considering a number of examples

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

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 53 |

Issue number | 6 |

Early online date | 11 Jun 2012 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- eigenvalue problem
- nonlinear equations
- Vakhnenko-Parkes equation

### Cite this

*Journal of Mathematical Physics*,

*53*(6). https://doi.org/10.1063/1.4726168

}

*Journal of Mathematical Physics*, vol. 53, no. 6. https://doi.org/10.1063/1.4726168

**Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations.** / Vakhnenko, V.O.; Parkes, E.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations

AU - Vakhnenko, V.O.

AU - Parkes, E.J.

PY - 2012

Y1 - 2012

N2 - The procedure for finding the solutions of the Vakhnenko-Parkes equation by meansof the inverse scattering method is described. The continuous spectrum is taken intoaccount in the associated eigenvalue problem. The suggested special form of thesingularity function for continuous part of the spectral data gives rise to the multimode solutions. The sufficient conditions are proved in order that these solutions become real functions. The interaction of the N periodic waves is studied. The procedure is illustrated by considering a number of examples

AB - The procedure for finding the solutions of the Vakhnenko-Parkes equation by meansof the inverse scattering method is described. The continuous spectrum is taken intoaccount in the associated eigenvalue problem. The suggested special form of thesingularity function for continuous part of the spectral data gives rise to the multimode solutions. The sufficient conditions are proved in order that these solutions become real functions. The interaction of the N periodic waves is studied. The procedure is illustrated by considering a number of examples

KW - eigenvalue problem

KW - nonlinear equations

KW - Vakhnenko-Parkes equation

UR - http://www.scopus.com/inward/record.url?scp=84863533939&partnerID=8YFLogxK

U2 - 10.1063/1.4726168

DO - 10.1063/1.4726168

M3 - Article

VL - 53

JO - Journal of Mathematical Physics

T2 - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -