A few integrable couplings of some integrable systems and (\(2 + 1\))-dimensional integrable hierarchies. (English) Zbl 1474.37083

Feng, Binlu; Zhang, Yufeng; Dong, Huanhe

Abstr. Appl. Anal. 2014, Article ID 932672, 9 p. (2014).

Summary: Two high-dimensional Lie algebras are presented for which four (\(1 + 1\))-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the AKNS hierarchy. Then (\(2 + 1\))-dimensional DS hierarchy is derived by using the TAH scheme; in particular, the integrable couplings of the DS hierarchy are obtained.

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
47B47	Commutators, derivations, elementary operators, etc.

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