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.
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.