Hamiltonian structures of a coupled Ramani equation

With the aid of Hamiltonian structures for the constrained modified KP flow, we show that a coupled Ramani equation is a bi-Hamiltonian system with a local Hamiltonian operator P¯2 and a symplectic operator. After a reduction, we recover the bi-Hamiltonian formalism of the Ramani equation. Furthermore, we obtain the explicit bi-Hamiltonian structure for the Drinfeld-Sokolov hierarchies of C3(1) using the local Hamiltonian operator P¯2.