| EPSRC Reference: |
GR/R23336/01 |
| Title: |
Algebro-Geometric Solutions Fo the Vector Nonlinear Schroder Equation; Applications To Nonlinear Optics |
| Principal Investigator: |
Elgin, Professor J |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
30 January 2001 |
Ends: |
29 January 2002 |
Value (£): |
9,735
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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 Vector Nonlinear Schrodinger equation (VNSE) usefully models the propagation of a polarised short pulse along an optical fibre. The vector nature of the dependent variable models the polarization state of the pulse. It is intended to study properties of the periodic solutions of this equation. As the spectral curve is trigonal for this system, rather than hyperelliptic as with the scalar case, existing formulae for the solutions are rather formal, and not very tractable for applications. We aim to use the formalism of Kleinian sigma-functions to obtain more effective formulae for the solutions. This approach should also permit us to investigate the special cases of these solutions which are expressible in terms of hyperelliptic or elliptic functions.The elliptic solutions can be approached another way, by studying the motion of their poles. These satisfy the Generalised Calogero-Moser system, with elliptic interparticle potential, confined to an invariant locus. We aim to describe this locus of elliptic solutions, comparing the two approaches.In both approaches, a third-order ode with elliptic coefficients, a generalisation of the Halphen equation, will appear as the spectral problem; our results will be compared with recent developments in this area.
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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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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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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.imperial.ac.uk |