THE BI-HAMILTONIAN STRUCTURE OF THE PERTURBATION EQUATIONS OF THE KDV HIERARCHY

Abstract The bi-Hamiltonian structure is established for the perturbation equations of the KdV hierarchy and the perturbation equations themselves also provide 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.

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