A finite-dimensional integrable system associated with a polynomial eigenvalue problem

Taixi Xu, Weihua Mu and Zhijun Qiao

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

M. Antonowicz and A. P. Fordy (1988) introduced the second-order polynomial eigenvalue problem L φ = ( ∂ 2 + ∑ i = 1 n v i λ i ) φ = α φ ( ∂ = ∂ / ∂ x , α = constant ) and discussed its multi-Hamiltonian structures. For n = 1 and n = 2 , the associated finite-dimensional integrable Hamiltonian systems (FDIHS) have been discussed by Xu and Mu (1990) using the nonlinearization method and Bargmann constraints. In this paper, we consider the general case, that is, n is arbitrary, provide the constrained Hamiltonian systems associated with the above-mentioned second-order polynomial ergenvalue problem, and prove them to be completely integrable.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:013479

DOI: 10.1155/IJMMS/2006/13479

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