Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy. (13th July 2014) - Shan, Zhengduo; Yang, Hongwei; Yin, Baoshu
Abstract : 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.