On the Differential Operators of the Generalized Fifth-order Korteweg-de Vries Equation
Lee, Chun-Te
Methods Appl. Anal., Tome 17 (2010) no. 1, p. 123-136 / Harvested from Project Euclid
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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.
Publié le : 2010-03-15
Classification:  Hamiltonian system,  nonlinear differential equation,  nonlinear partial differential equation,  fifth-order KdV equation,  Ito equation,  Sawada-Kotera equation,  Caudrey-Dodd-Gibbon equation,  Kaup-Kupershmidt equation,  Lax equation,  Jacobi identity,  skew-adjoint operator,  prolongation,  37K10,  37K05,  35Q53,  35G20,  35L05,  47J35 
@article{1291644611,
     author = {Lee, Chun-Te},
     title = {On the Differential Operators of the Generalized Fifth-order Korteweg-de Vries Equation},
     journal = {Methods Appl. Anal.},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 123-136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1291644611}
}

Lee, Chun-Te. On the Differential Operators of the Generalized Fifth-order Korteweg-de Vries Equation. Methods Appl. Anal., Tome 17 (2010) no. 1, pp.  123-136. http://gdmltest.u-ga.fr/item/1291644611/