| EPSRC Reference: |
GR/S47335/01 |
| Title: |
Discrete Soliton Train Dynamics |
| Principal Investigator: |
Rothos, Professor VM |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 June 2003 |
Ends: |
31 August 2003 |
Value (£): |
3,639
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| Communications |
Electronics |
| Pharmaceuticals and Biotechnology |
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Summary on Grant Application Form |
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Localised excitations in nonlinear discrete systems are described, as a rule, by non-integrable equations, and their study demands extensive numerics. Contrary, we intend to exploit the existence of integrable discretisations of continuous soliton equations. The proposed research is aimed to extend, as far as possible, the applicability of analytical methods to study dynamics of solitons in near-integrable nonlinear discrete systems.A novelty of our research consisits in a consideration of N-soliton trains (ordered sequences of N discrete solitons), rather than a single soliton, wit account for mutual interaction between neighboring solitons caused by their tail overlapping. In the continuous case, positions of soliton maxima with the train are governed by the complex Toda chain model. We will verify the hypothesis of universality of the Toda model formulated for continuous equations, on an example of the Ablowitz-Ladik equation, both scalar and vector. We expect to reveal novel features in dynamics due to appearance two spatial parameters - intersoliton distance and lattice spacing. As a byproduct of the research, we will develop, for the first time, a discrete vector soliton perturbation theory.
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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.le.ac.uk |