The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy

Abstract

The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian integrable hierarchy is proposed and a remark is given for a generalization of the resulting perturbation equations to $1+2$ dimensions.

9 pages, Latex, submitted to Phys. Lett. A

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