Two-component generalizations of the Camassa-Holm equation
journal contributionposted 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.
Read the paper on the publisher website
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