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

VL - 193

SP - 245

EP - 268

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -