| EPSRC Reference: |
GR/L99036/01 |
| Title: |
CLASSIFICATION OF CLASSICAL AND QUANTUM INTEGRABLE SYSTEMS |
| 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: |
18 March 1998 |
Ends: |
17 March 1999 |
Value (£): |
5,350
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| EPSRC Research Topic Classifications: |
| Mathematical Physics |
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 most efficient approach at the classification of integrable 1+1 evolution equations is based on the existence of generalised (or higher) symmetries. This approach has been developed by PJ Olver, AB Shabat, A Focas, VV Sokolov, AV Michailov and others. Our aim is to generalise this approach to the quantum case. This means that we will consider evolution equations with right hand side that are non-commutative polynomials of unknown functions and their x-derivatives. In a recent paper by PJ Olver and VV Sokolov (submitted to CMP and included in this application) it is observed that all known examples of integrable non-commutative evolution equations posses generalised symmetries. Choosing this property for a criterion of integrability, we are planning to investigate different special types of classical and quantum polynomial evolution equations. We will use REDUCE and Mathematica computer algebra programs for computation. The program CRACK will not only be applied but also extended by a module for a more efficient generalised separation which plays a key role in handling weakly overdetermined PDE-systems efficiently. As the complexity of calculations to bring a PDE-system into involutive form depends highly on the ordering of derivatives that is used, a PhD student of T. Wolf, A. Triulzi, is currently working on Algorithms and programs to run computations wrt. different orderings in parallel. The problems to be investigated with VV Sokolov will be a good test and application of this.
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Key Findings |
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Potential use in non-academic contexts |
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| Description |
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Sectors submitted by the Researcher |
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