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CLASSIFICATION OF INTEGRABLE ONE-COMPONENT SYSTEMS ON ASSOCIATIVE ALGEBRAS

Published online by Cambridge University Press:  03 November 2000

PETER J. OLVER  and
JING PING WANG
PETER J. OLVER
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
JING PING WANG
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

This paper is devoted to the complete classification of integrable one-component evolution equations whose field variable takes its values in an associative algebra. The proof that the list of non-commutative integrable homogeneous evolution equations is complete relies on the symbolic method. Each equation in the list has infinitely many local symmetries and these can be generated by its recursion (recursive) operator or master symmetry. 1991 Mathematics Subject Classification: 13A50, 16-XX, 22E70, 35A30, 35Q53, 58F07.

Keywords

associative algebranon-commutativeintegrablesolitonevolution equationsymmetry grouprecursion operatorsymbolic methoddifferential polynomialoperator symmetry
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 81 , Issue 3 , November 2000 , pp. 566 - 586
Copyright
2000 London Mathematical Society

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