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Journal of Mathematical Sciences

, Volume 88, Issue 2, pp 292–305 | Cite as

Poisson structures and integrable systems connected with graphs

  • A. L. Pirozerskii
Article
  • 21 Downloads

Abstract

Completely integrable systems related with graphs of a specific type are studied by the r-matrix method. The phase space of such a system is the space of connections on a graph. The nonlinear equations under consideration are Hamiltonian with respect to the Poisson bracket depending on the geometry of the graph and other structures. It is essential that the Poisson bracket be nonultralocal. An involute family of motion integrals is constructed. Explicit formulas for solutions of evolution equations are obtained in terms of solutions of a factorization problem. In the case of the group of loops, a polynomial anzatz for the Lax operator compatible with the Poisson bracket is constructed. Bibliography: 8 titles.

Keywords

Phase Space Evolution Equation Nonlinear Equation Integrable System Explicit Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. L. Pirozerskii

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