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Integrable Evolution Equations on Associative Algebras

Authors :
Olver, Peter J.
Sokolov, Vladimir V.
Source :
Communications in Mathematical Physics; 19980401, Vol. 193 Issue: 2 p245-268, 24p
Publication Year :
1998

Abstract

Abstract:: 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 Painlev� transcendent equations. The basic theory of Hamiltonian structures for associative algebra-valued systems is developed and the biHamiltonian structures for several examples are found.

Details

Language :
English
ISSN :
00103616 and 14320916
Volume :
193
Issue :
2
Database :
Supplemental Index
Journal :
Communications in Mathematical Physics
Publication Type :
Periodical
Accession number :
ejs453733
Full Text :
https://doi.org/10.1007/s002200050328