Poisson structures and integrable systems connected with graphs

Standard

Poisson structures and integrable systems connected with graphs. / Pirozerskii, A. L.

In: Journal of Mathematical Sciences , Vol. 88, No. 2, 1998, p. 292-305.

Research output: Contribution to journal › Article › peer-review

Author

Pirozerskii, A. L. / Poisson structures and integrable systems connected with graphs. In: Journal of Mathematical Sciences . 1998 ; Vol. 88, No. 2. pp. 292-305.

BibTeX

@article{8705e52d71024f759d0433e390ac14e7,

title = "Poisson structures and integrable systems connected with graphs",

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.",

author = "Pirozerskii, {A. L.}",

year = "1998",

doi = "10.1007/BF02364991",

language = "English",

volume = "88",

pages = "292--305",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Poisson structures and integrable systems connected with graphs

AU - Pirozerskii, A. L.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=54749130826&partnerID=8YFLogxK

U2 - 10.1007/BF02364991

DO - 10.1007/BF02364991

M3 - Article

AN - SCOPUS:54749130826

VL - 88

SP - 292

EP - 305

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 73242479