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C. Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy. (English) Zbl 0719.35082

Summary: Under two different constraints between the potentials and the eigenfunctions, the eigenvalue problem associated with the coupled KdV hierarchy is nonlinearised to be a completely integrable C Neumann system on the tangent bundle of sphere \(TS^{N-1}\) with the Hamiltonian \[ H^*=-<\Lambda q,p>-<q,q><p,p>+<q,p>^ 2+<q,p><\Lambda p,p> \] and a completely integrable C Neumann system \(({\mathbb{R}}^{2N},dp\wedge dq,H)\) with the Hamiltonian \[ H=-<\Lambda q,p>+<p,p,><q,p>-<q,q> \] respectively. The involutive solutions of the coupled KdV equation associated with the two systems are given.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35P99 Spectral theory and eigenvalue problems for partial differential equations
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