In this paper, we present the differential operators of the generalized fifth-order KdV equation. We give formal proofs on the Hamiltonian property including the skew-adjoint property and Jacobi identity by the use of prolongation method. Our results show that there are five 3-order Hamiltonian operators, which can be used to construct the Hamiltonians, and no 5-order operators are shown to pass the Hamiltonian test, although there are infinite number of them, and are skew-adjoint.
"On the Differential Operators of the Generalized Fifth-order Korteweg-de Vries Equation." Methods Appl. Anal. 17 (1) 123 - 136, March 2010.