Relationship between the restricted AKNS flows and the restricted KdV flows

Abstract

It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Garnier system and the generalized multicomponent Hénon-Hieles system, are a kind of special reductions of the restricted AKNS flows.

Keywords

The restricted AKNS flow / The restricted KdV flow / Nonlinearization of spectral problem / Reduction condition / Integrable Hamiltonian system

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