| EPSRC Reference: |
GR/M69548/01 |
| Title: |
INTEGRABLE SCHRODINGER EQUATIONS IN MANY DIMENSIONS AND HADAMARD'S PROBLEMS |
| Principal Investigator: |
Veselov, Professor A |
| Other Investigators: |
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| Project Partners: |
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| Department: |
School of Mathematics |
| Organisation: |
Loughborough University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
21 February 2000 |
Ends: |
20 May 2003 |
Value (£): |
125,782
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The Huygens' Principle is one of the most fundamental properties of wave propagation in real physical space. Its mathematical theory has been created by J. Hadamard, who posed the problem of the description of all second-order hyperbolic equations satisfying this principle in the so-called narrow Hadamard sense.The aim of this project is to apply to this famous long-standing problem the ideas and methods of the theory of integrable systems. The proposed approach is based on the relation between Hadamard's criterion for the Huygens' Principle and the trivial monodromy property for the Schrodinger equations with the rational potentials in the complex domain. It has been proven recently that the last property implies the Huygens' Principle, to prove the inverse statement is one of the goals of this project. This would reduce the Hadamard's problem in the multidimensional Minkowski space to the description of all integrable Schrodinger operators with the rational potentials in many dimensions. Such a description, which is of a great interest itself, is the main purpose of the project.Several important steps in this direction have already been done by the proposer and his collaborators.
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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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| Date Materialised |
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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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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.lboro.ac.uk |