| EPSRC Reference: |
GR/T22223/01 |
| Title: |
Boundary Value Problems for Multidimensional Nonlinear PDEs |
| Principal Investigator: |
Fokas, Professor A |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Applied Maths and Theoretical Physics |
| Organisation: |
University of Cambridge |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2004 |
Ends: |
30 June 2008 |
Value (£): |
140,324
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| EPSRC Research Topic Classifications: |
| 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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A new method for studying boundary value problems for integrable PDEs in two dimensions has been introduced recently by the PI. Examples of integrable equations are linear PDEs with constant coefficients, certain classes of linear PDEs with variable coefficients and the usual nonlinear integrable PDEs, such as the nonlinear Schroedinger and the Korteweg de Vries equations. Here we propose to solve linear PDEs with variable coefficients on the half line, as well as to extend the above method to multidimensional nonlinear PDEs, such as the Davey-Stewartson and the Kadomtsev-Petviashvilli equations. These latter equations are physically significant integrable multidimensional generalisations of the Schrodinger and the Korteweg de Vries equations respectively. We also intent to investigate one of the central problems of integrability, namely the existence of integrable nonlinear evolution PDEs in more than two spatial dimensions.
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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.cam.ac.uk |