Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (<i>n</i>, <i>m</i>)<sup>th</sup> KdV Hierarchy
Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (<i>n</i>, <i>m</i>)<sup>th</sup> KdV Hierarchy
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 Z 2 -valued case is analyzed in detail.Its Hamiltonian structures and recursion operator are derived.Infinitely many symmetries, conservation laws and explicit …