Bi-Hamiltonian ordinary differential equations with matrix variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 26-32
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We consider a special class of Poisson brackets related to systems of
ordinary differential equations with matrix variables. We investigate
general properties of such brackets, present an example of a compatible pair
of quadratic and linear brackets, and find the corresponding hierarchy of
integrable models, which generalizes the two-component Manakov matrix system
to the case of an arbitrary number of matrices.
Keywords:
integrable ordinary differential equation with matrix unknowns,
bi-Hamiltonian formalism, Manakov model.
@article{TMF_2012_171_1_a2,
author = {A. V. Odesskii and V. N. Rubtsov and V. V. Sokolov},
title = {Bi-Hamiltonian ordinary differential equations with matrix variables},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {26--32},
publisher = {mathdoc},
volume = {171},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a2/}
}
TY - JOUR AU - A. V. Odesskii AU - V. N. Rubtsov AU - V. V. Sokolov TI - Bi-Hamiltonian ordinary differential equations with matrix variables JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2012 SP - 26 EP - 32 VL - 171 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a2/ LA - ru ID - TMF_2012_171_1_a2 ER -
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A. V. Odesskii; V. N. Rubtsov; V. V. Sokolov. Bi-Hamiltonian ordinary differential equations with matrix variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 26-32. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a2/