Two-component generalizations of the Camassa-Holm equation
journal contributionposted on 09.01.2017 by Andrew N.W. Hone, V.S. Novikov, Jing Ping Wang
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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.
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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.
- Mathematical Sciences