The Integrability of New Two-Component KdV Equation

[摘要] 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.

[关键词] KdV equation;Lax representation;integrability;supersymmetry