A novel nonlinear evolution equation integrable by the inverse scattering method

V.O. Vakhnenko, E.J. Parkes

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Abstract

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.
LanguageEnglish
Title of host publicationProceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics
EditorsA.G. Nikitin, V.M. Boyko, R.O. Popovych
Place of PublicationKyiv, Ukraine
Pages384-391
Number of pages7
Volume43
Publication statusPublished - 2002
EventFourth International Conference on Symmetry in Nonlinear Mathematical Physics - Kyiv, Ukraine
Duration: 9 Jul 200115 Jul 2001

Publication series

NameProceedings of Institute of Mathematics of NAS of Ukraine
PublisherInstitute of Mathematics of NAS of Ukraine

Conference

ConferenceFourth International Conference on Symmetry in Nonlinear Mathematical Physics
CountryUkraine
CityKyiv
Period9/07/0115/07/01

Fingerprint

nonlinear evolution equations
inverse scattering
eigenvalues
solitary waves

Keywords

  • evolution equation
  • inverse scattering
  • Vakhnenko equation

Cite this

Vakhnenko, V. O., & Parkes, E. J. (2002). A novel nonlinear evolution equation integrable by the inverse scattering method. In A. G. Nikitin, V. M. Boyko, & R. O. Popovych (Eds.), 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.
Vakhnenko, V.O. ; Parkes, E.J. / A novel nonlinear evolution equation integrable by the inverse scattering method. Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics. editor / A.G. Nikitin ; V.M. Boyko ; R.O. Popovych. Vol. 43 Kyiv, Ukraine, 2002. pp. 384-391 (Proceedings of Institute of Mathematics of NAS of Ukraine).
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title = "A novel nonlinear evolution equation integrable by the inverse scattering method",
abstract = "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.",
keywords = "evolution equation, inverse scattering, Vakhnenko equation",
author = "V.O. Vakhnenko and E.J. Parkes",
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Vakhnenko, VO & Parkes, EJ 2002, A novel nonlinear evolution equation integrable by the inverse scattering method. in AG Nikitin, VM Boyko & RO Popovych (eds), 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.

Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics. ed. / A.G. Nikitin; V.M. Boyko; R.O. Popovych. Vol. 43 Kyiv, Ukraine, 2002. p. 384-391 (Proceedings of Institute of Mathematics of NAS of Ukraine).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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AU - Parkes, E.J.

PY - 2002

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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.

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KW - inverse scattering

KW - Vakhnenko equation

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M3 - Conference contribution book

SN - 9660224869

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T3 - Proceedings of Institute of Mathematics of NAS of Ukraine

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

A2 - Nikitin, A.G.

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A2 - Popovych, R.O.

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Vakhnenko VO, Parkes EJ. A novel nonlinear evolution equation integrable by the inverse scattering method. In Nikitin AG, Boyko VM, Popovych RO, editors, Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics. Vol. 43. Kyiv, Ukraine. 2002. p. 384-391. (Proceedings of Institute of Mathematics of NAS of Ukraine).