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March 2010 On the Differential Operators of the Generalized Fifth-order Korteweg-de Vries Equation
Chun-Te Lee
Methods Appl. Anal. 17(1): 123-136 (March 2010).


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.


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Chun-Te Lee. "On the Differential Operators of the Generalized Fifth-order Korteweg-de Vries Equation." Methods Appl. Anal. 17 (1) 123 - 136, March 2010.


Published: March 2010
First available in Project Euclid: 6 December 2010

zbMATH: 1218.37089
MathSciNet: MR2735103

Primary: 35G20 , 35L05 , 35Q53 , 37K05 , 37K10 , 47J35

Keywords: Caudrey-Dodd-Gibbon equation , fifth-order KdV equation , Hamiltonian system , Ito equation , Jacobi identity , Kaup-Kupershmidt equation , Lax equation , nonlinear differential equation , nonlinear partial differential equation , prolongation , Sawada-Kotera equation , skew-adjoint operator

Rights: Copyright © 2010 International Press of Boston


Vol.17 • No. 1 • March 2010
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