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Classification of Integrable One‐Component Systems on Associative Algebras
Author(s) -
Olver Peter J.,
Wang Jing Ping
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012582
Subject(s) - mathematics , integrable system , associative property , associative algebra , component (thermodynamics) , algebra over a field , homogeneous space , recursion (computer science) , commutative property , pure mathematics , field (mathematics) , algebraic number , symmetry (geometry) , division algebra , algebra representation , mathematical analysis , algorithm , physics , thermodynamics , geometry
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.