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A new multi-component hierarchy and its integrable expanding model. (English) Zbl 1146.37352

Summary: A set of multi-component matrix Lie algebra is constructed, it follows that a type of new loop algebra is presented and multi-component integrable hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system is worked out. As reduction of the hierarchy, some well-known hierarchy such as DNLS, KN, CLL hierarchy are established.

MSC:

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