Integrable Evolution Equations on Associative Algebras

被引：0

作者：

Peter J. Olver

Vladimir V. Sokolov

机构：

[1] School of Mathematics,

[2] University of Minnesota,undefined

[3] Minneapolis,undefined

[4] MN 55455,undefined

[5] USA.¶E-mail: olver@ima.umn.edu,undefined

[6] http://www.math.umn.edu/∼olver,undefined

[7] Ufa Mathematical Institute,undefined

[8] Russian Academy of Sciences,undefined

[9] Chernyshevski str. 112,undefined

[10] 450000,undefined

[11] Ufa,undefined

[12] Russia. E-mail: sokolov@imat.rb.ru,undefined

来源：

Communications in Mathematical Physics | 1998年 / 193卷

关键词：

Evolution Equation; Integrable System; Basic Theory; Field Variable; Associative Algebra;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：245 / 268

页数：23