The Integrability of New Two-Component KdV Equation

We consider the bi-Hamiltonian representation of the two-component coupled KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov. Connection of this equation with the supersymmetric Kadomtsev–Petviashvilli–Radul–Manin hierarchy is presented. For this new supersymmetric equation the Lax representation and odd Hamiltonian structure is given.