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

Xu, Taixi; Mu, Weihua; Qiao, Zhijun

doi:https://doi.org/10.1155/IJMMS/2006/13479

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 013479 | https://doi.org/10.1155/IJMMS/2006/13479

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

Taixi Xu,¹Weihua Mu,²and Zhijun Qiao³

Received06 Feb 2006

Accepted21 Mar 2006

Published25 May 2006

Abstract

M. Antonowicz and A. P. Fordy (1988) introduced the second-order polynomial eigenvalue problem Lφ=(∂2+∑i=1nviλi)φ=αφ(∂=∂/∂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.

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Copyright

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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