The Semidirect Sum of Lie Algebras and Its Applications to C-KdV Hierarchy

Abstract

By use of the loop algebra $\widetilde{\stackrel{-}{G}}$, integrable coupling of C-KdV hierarchy and its bi-Hamiltonian structures are obtained by Tu scheme and the quadratic-form identity. The method can be used to produce the integrable coupling and its Hamiltonian structures to the other integrable systems.