With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
"Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy." Abstr. Appl. Anal. 2014 (SI31) 1 - 7, 2014. https://doi.org/10.1155/2014/678725