| EPSRC Reference: |
GR/R88885/02 |
| Title: |
long-time dynamics of localised structures in the modified nls and massive thirring models |
| Principal Investigator: |
Rothos, Professor VM |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 November 2002 |
Ends: |
31 May 2003 |
Value (£): |
3,673
|
| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
|
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The aim of this proposal is to study existence and stability of coherent localized structure in nonlinear wave equations and to understand the links between methods of partial differential equations (PDEs) and those of dynamical systems theory. Specifically, we focus on global time behavior of the modified NLS equation and the massive Thirring model (MTM), as well as their perturbations and generalizations. We employ the fad that these soliton equations are, in some special cases, completely integrable Hamiltonian systems n infinite dimensions, solvable by means of spectral theory of linear differential operators (ZakharovShabat operators and generalizations). The integrable PDE examples illustrate rich and fascinating global behavior of the localised structures. However, they do not indicate the generality of the phenomena. Once integrability is broken by a perturbation (dissipative or Hamiltonian) of the equation, properties of localised solutions are unknown. We analyze stability and persistence of localized solutions in unbounded and periodic bounded spatial domain, with important physical applications in photonic crystals, nonlinear optics, and fluid mechanics.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.le.ac.uk |