### Abstract

Language | English |
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Title of host publication | Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics |

Editors | A.G. Nikitin, V.M. Boyko, R.O. Popovych |

Place of Publication | Kyiv, Ukraine |

Pages | 384-391 |

Number of pages | 7 |

Volume | 43 |

Publication status | Published - 2002 |

Event | Fourth International Conference on Symmetry in Nonlinear Mathematical Physics - Kyiv, Ukraine Duration: 9 Jul 2001 → 15 Jul 2001 |

### Publication series

Name | Proceedings of Institute of Mathematics of NAS of Ukraine |
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Publisher | Institute of Mathematics of NAS of Ukraine |

### Conference

Conference | Fourth International Conference on Symmetry in Nonlinear Mathematical Physics |
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Country | Ukraine |

City | Kyiv |

Period | 9/07/01 → 15/07/01 |

### Fingerprint

### Keywords

- evolution equation
- inverse scattering
- Vakhnenko equation

### Cite this

*Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics*(Vol. 43, pp. 384-391). (Proceedings of Institute of Mathematics of NAS of Ukraine). Kyiv, Ukraine.

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*Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics.*vol. 43, Proceedings of Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine, pp. 384-391, Fourth International Conference on Symmetry in Nonlinear Mathematical Physics, Kyiv, Ukraine, 9/07/01.

**A novel nonlinear evolution equation integrable by the inverse scattering method.** / Vakhnenko, V.O.; Parkes, E.J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - A novel nonlinear evolution equation integrable by the inverse scattering method

AU - Vakhnenko, V.O.

AU - Parkes, E.J.

PY - 2002

Y1 - 2002

N2 - A Backlund transformation for an evolution equation (ut+u ux)x+u=0 transformed into new coordinates is derived. An inverse scattering problem is formulated. The inverse scattering method has a third order eigenvalue problem. A procedure for finding the exact N-soliton solution of the Vakhnenko equation via the inverse scattering method is described.

AB - A Backlund transformation for an evolution equation (ut+u ux)x+u=0 transformed into new coordinates is derived. An inverse scattering problem is formulated. The inverse scattering method has a third order eigenvalue problem. A procedure for finding the exact N-soliton solution of the Vakhnenko equation via the inverse scattering method is described.

KW - evolution equation

KW - inverse scattering

KW - Vakhnenko equation

UR - http://www.imath.kiev.ua/~symmetry/Symmetry2001/Vakhnenko384-391.pdf

UR - http://www.imath.kiev.ua/~appmath/proc01.html

M3 - Conference contribution book

SN - 9660224869

VL - 43

T3 - Proceedings of Institute of Mathematics of NAS of Ukraine

SP - 384

EP - 391

BT - Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics

A2 - Nikitin, A.G.

A2 - Boyko, V.M.

A2 - Popovych, R.O.

CY - Kyiv, Ukraine

ER -