TY - JOUR
T1 - Integrable evolution equations on associative algebras
AU - Olver, Peter J.
AU - Sokolov, Vladimir V.
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1998/4/3
Y1 - 1998/4/3
N2 - This paper surveys the classification of integrable evolution equations whose field variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued systems. A variety of new examples of integrable systems possessing higher order symmetries are presented. Symmetry reductions lead to an associative algebra-valued version of the Painlevé transcendent equations. The basic theory of Hamiltonian structures for associative algebra-valued systems is developed and the biHamiltonian structures for several examples are found.
AB - This paper surveys the classification of integrable evolution equations whose field variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued systems. A variety of new examples of integrable systems possessing higher order symmetries are presented. Symmetry reductions lead to an associative algebra-valued version of the Painlevé transcendent equations. The basic theory of Hamiltonian structures for associative algebra-valued systems is developed and the biHamiltonian structures for several examples are found.
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U2 - 10.1007/s002200050328
DO - 10.1007/s002200050328
M3 - Article
AN - SCOPUS:0032478456
SN - 0010-3616
VL - 193
SP - 245
EP - 268
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -