Nonlinear integrable couplings of Levi hierarchy and WKI hierarchy. (English) Zbl 1474.37086

Shan, Zhengduo; Yang, Hongwei; Yin, Baoshu

Abstr. Appl. Anal. 2014, Article ID 678725, 7 p. (2014).

Summary: 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.

MSC:

37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B80	Applications of Lie algebras and superalgebras to integrable systems
37K30	Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures

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