# Details of Grant

EPSRC Reference: GR/M95714/01
Title: THE SYMMETRY TEST TO INTEGRABLE SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Principal Investigator: Wolf, Dr T
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Sch of Mathematical Sciences
Organisation: Queen Mary University of London
Scheme: Standard Research (Pre-FEC)
Starts: 23 January 2000 Ends: 22 January 2001 Value (£): 5,400
EPSRC Research Topic Classifications:
 Logic & Combinatorics Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:
 No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
The aim is to generalise the symmetry approach to the case of multi-component systems of ODEs. If the number of components of an ODE-system increases, any investigations like the computation of integrability conditions soon become impossible due to expression swell. Instead of dealing with high dimensional ODE-systems we consider ODEs where the unknown is a member of a free associative algebra. For example, the system $U_t=C U^2-U^2 C$ describes an Euler top if $U, C$ are 3 by 3 matrices, the unknown $U$ is skew-symmetric and $U$ is diagonal and constant. Systems are considered integrable if they have infinitely many symmetries, like the above having an infinite series of commuting flows $U-{t-n}=P-n (U, C), where$P-n$are (non commutative) polynomials of$U$and$C$. Replacing the free associative algebra by finite dimensional algebras, (like the algebra of$n\times n\$ matrices, or the Clifford algebra) many integrable systems result. The principal target of the project is an exhaustive description and classification of the most important groups of top-like systems.
Key Findings
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