Hone_2017_Nonlinearity_30_622.pdf (2.25 MB)
Two-component generalizations of the Camassa-Holm equation
journal contribution
posted on 2017-01-09, 10:15 authored by Andrew N.W. Hone, V.S. Novikov, Jing Ping WangA 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
NonlinearityVolume
30Issue
2Pages
622 - 658Citation
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 SocietyVersion
- 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
2016-12-19Publication date
2017-01-09Notes
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
0951-7715eISSN
1361-6544Publisher version
Language
- en
