Abstract
An isospectral problem is established based on loop algebra X ∼ , by making use of the generalized Tu scheme the multi-component Liouville integrable dispersive long wave (DLW) equation hierarchy is obtained. Then, two expanding loop algebra F ∼ M and Y ∼ are presented, which devoted to working out two integrable couplings of the multi-component DLW equation hierarchy. Finally, the Hamiltonian structures of the multi-component DLW equation hierarchy and the second integrable couplings are obtained by employing the trace variational identity.
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