| EPSRC Reference: |
GR/S58256/01 |
| Title: |
Multisymplectic structures, n-symplectic geometry, relative equilibria and nonlinear PDEs on manifolds |
| Principal Investigator: |
Bridges, Professor TJ |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Sch of Electronics & Physical Sciences |
| Organisation: |
University of Surrey |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
07 February 2004 |
Ends: |
06 June 2005 |
Value (£): |
8,152
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
| 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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It is now clear from work at Surrey that multisymplectic structures, which is a generalisation of symplectic structures, is a natural framework for the analysis of Hamiltonian PDEs that arise in pattern formation. On the other hand, there has been considerable development of Lagrangian, Hamilto and multisymplectic frameworks for PDEs on manifolds. However, all these theories require a Lagrangian as a starting point, and Lagrangians for that arise in applications are predominantly degenerate, or based on higher order fields. Recently, however the n-symplectic geometry of Norris ar Lawson has arisen as a likely candidate for a satisfactory general approach to the geometric aspects of multisymplectic structures. This framework, allows development of the a framework for nonlinear PDEs based on geometry alone, without requiring a Lagrangian. This project will use this gec to develop a framework for nonlinear PDEs on manifolds. Concepts such as multisymplectic relative equilibria can then be generalised to PDEs or manifolds. The prototype applications which will guide the project are nonlinear wave equations on pseudo-Riemannian manifolds, and the nonline Laplace-Beltrami operator on a sphere.
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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 |
| Summary |
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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.surrey.ac.uk |