Abstract
We introduce Frobenius algebra ℱ-valued (n,m)th KdV hierarchy and construct its bi-Hamiltonian structures by employing ℱ-valued pseudo-differential operators. As an illustrative example, the (1, 1)th {xxxℱ2-valued case is analyzed in detail. Its Hamiltonian structures and recursion operator are derived. Infinitely many symmetries, conservation laws and explicit flow equations are also obtained.
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