By use of the loop algebra , integrable coupling of C-KdV hierarchy and its bi-Hamiltonian structures are obtained by Tu scheme and the quadratic-form identity. The method can be used to produce the integrable coupling and its Hamiltonian structures to the other integrable systems.
Xia Dong. Tiecheng Xia. Desheng Li. "The Semidirect Sum of Lie Algebras and Its Applications to C-KdV Hierarchy." Abstr. Appl. Anal. 2014 (SI31) 1 - 6, 2014. https://doi.org/10.1155/2014/295068