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A generating function proof of the commutativity of certain Hamiltonian isospectral flows

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Abstract

In a paper by Adams, Harnad, and Previato, a ring of Poisson commuting functions which produce isospectral Hamiltonian flows on a space of matrices was described and these flows were related to solutions of associated nonlinear partial differential equations (e.g., the Korteweg-deVries, nonlinear Schrödinger, and Boussinesq equations). In this Letter, we give an alternate proof of the Poisson commutativity of this ring of functions by means of a generating function argument.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, 30602, Athens, GA, USA

    M. R. Adams

  2. Département de mathématiques appliquées, École Polytechnique, C.P. 6079, Succ. ‘A’, H3C 3A7, Montréal, Québec, Canada

    J. Harnad

Authors
  1. M. R. Adams
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  2. J. Harnad
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Additional information

This research was partially supported by NSF grant DMS-8601995, U.S. Army grant DAAL03-87-K-0110, and the Natural Sciences and Engineering Research Council of Canada.

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Adams, M.R., Harnad, J. A generating function proof of the commutativity of certain Hamiltonian isospectral flows. Lett Math Phys 16, 269–272 (1988). https://doi.org/10.1007/BF00398964

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  • DOI: https://doi.org/10.1007/BF00398964

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