EPSRC Reference: 
GR/M95714/01 
Title: 
THE SYMMETRY TEST TO INTEGRABLE SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS 
Principal Investigator: 
Wolf, Dr T 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Sch of Mathematical Sciences 
Organisation: 
Queen Mary University of London 
Scheme: 
Standard Research (PreFEC) 
Starts: 
23 January 2000 
Ends: 
22 January 2001 
Value (£): 
5,400

EPSRC Research Topic Classifications: 
Logic & Combinatorics 
Nonlinear 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 multicomponent systems of ODEs. If the number of components of an ODEsystem increases, any investigations like the computation of integrability conditions soon become impossible due to expression swell. Instead of dealing with high dimensional ODEsystems we consider ODEs where the unknown is a member of a free associative algebra. For example, the system $U_t=C U^2U^2 C$ describes an Euler top if $U, C$ are 3 by 3 matrices, the unknown $U$ is skewsymmetric 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{tn}=Pn (U, C), where $Pn$ 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 toplike systems.

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