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Vector loop algebra and its applications to integrable system. (English) Zbl 1106.37045
Summary: We propose a vector loop algebra and its extended loop algebra to obtain the dispersive long wave (DLW) hierarchy. By making use of the extended trace identity and the quadratic-form identity, the Hamiltonian structures of the DLW hierarchy and its integrable coupling are constructed, respectively.

##### 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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