Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)th KdV Hierarchy. Issue 3 (3rd July 2017) - Zhang, Hai
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 -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.