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Two-component generalizations of the Camassa-Holm equation

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journal contribution
posted on 09.01.2017, 10:15 by Andrew N.W. Hone, V.S. Novikov, Jing Ping Wang
A classification of integrable two-component systems of non-evolutionary partial dif- ferential equations that are analogous to the Camassa-Holm equation is carried out via the perturbative symmetry approach. Independently, a classification of compatible pairs of Hamiltonian operators of specific forms is carried out, in order to obtain bi-Hamiltonian structures for the same systems of equations. Using reciprocal transformations, some exact solutions and Lax pairs are also constructed for the systems considered.

Funding

ANWH is supported by Fellowship EP/M004333/1 from the Engineering and Physical Sciences Research Council (EPSRC). JPW and VN were partially supported by Research in Pairs grant no. 41418 from the London Mathematical Society; JPW was supported by the EPSRC grant EP/1038659/1.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Volume

30

Issue

2

Pages

622 - 658

Citation

HONE, A.N.W., NOVIKOV, V.S. and WANG, J.P., 2017. Two-component generalizations of the Camassa-Holm equation. Nonlinearity, 30(2), pp. 622-658.

Publisher

© IOP Publishing Ltd & London Mathematical Society

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/

Acceptance date

19/12/2016

Publication date

2017-01-09

Notes

This is an Open Access Article. It is published by IOP Publishing under the Creative Commons Attribution 3.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/

ISSN

0951-7715

eISSN

1361-6544

Language

en

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