| EPSRC Reference: |
GR/M95714/01 |
| Title: |
THE SYMMETRY TEST TO INTEGRABLE SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS |
| Principal Investigator: |
Wolf, Dr T |
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| 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
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| EPSRC Research Topic Classifications: |
| Logic & Combinatorics |
Non-linear Systems Mathematics |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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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.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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