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A generalized Boite-Pempinelli-Tu (BPT) hierarchy and its bi-Hamiltonian structure. (English) Zbl 1027.37042
Summary: A subalgebra of loop algebra $$\widetilde A_1$$ is presented. It follows that a new Liouville integrable hierarchy with 6 potential functions, which possesses a bi-Hamiltonian structure, is obtained. Since it can reduce to Boite-Pempinelli-Tu (BPT) hierarchy, we call it a generalized BPT system. Two symplectic operators of the system obtained are directly derived from recurrence relations, not from a recurrence operator. As a reduction case, the famous KdV-mKdV equation is given.

##### MSC:
 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations)
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