| EPSRC Reference: |
GR/R02719/01 |
| Title: |
A Global Approach To Understanding Localised Structures In Nonlinear Dispersive Wave Systems |
| Principal Investigator: |
Champneys, Professor AR |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Engineering Mathematics and Technology |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
15 January 2001 |
Ends: |
14 January 2003 |
Value (£): |
60,026
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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Summary on Grant Application Form |
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Geometric, or qualitative, theory has proven to be extremely useful for understanding the long-time behaviour of finite-dimensional dynamical systems, with most progress arising when this is allied to both local analysis and numerical methods. The aim of this proposal is to apply this same combined methodology to understanding the long-time dynamics and existence of coherent localised structures in conservative (and near conservative) nonlinear partial differential equations (PDEs) and their approximation by discrete lattices. Such questions are the subject of much current interest, with important physical applications in nonlinear optics, molecular vibrations and fluid mechanics. The novelty lies in the approach taken which is to combine the expertise of the two co-PI's in local ('near integrable' and Mel'nikov-type) and global (qualitative and numerical) methods. There will also be a healthy mix of rigour and formal mathematics. Several concrete problems will be tackled with this approach including ones where localisation occurs in either space or time, and where the underlying model is either a PDE or coupled set of discrete lattice ODEs. Global dynamics, nonlinear dispersive waves, coherent structure, lattices
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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.bris.ac.uk |