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EPSRC Reference: GR/M61450/01
Title: COHERENT STRUCTURES AND THE ASYMPTOTIC BEHAVIOUR OF NONLINEAR INTEGRABLE MULTIDIMENSIONAL EQUATIONS
Principal Investigator: Fokas, Professor A
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Dept of Mathematics
Organisation: Imperial College London
Scheme: Standard Research (Pre-FEC)
Starts: 01 May 1999 Ends: 31 December 2001 Value (£): 117,320
EPSRC Research Topic Classifications:
Numerical Analysis
EPSRC Industrial Sector Classifications:
Electronics No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
There exist physically important nonlinear evolution equations which can be treated analytically through the so-called inverse scattering (or inverse spectral) method. The best known such equations are the Korteweg-deVries (KdV) and the nonlinear Schroedinger (NLS) equations; their physical two-space generalisations are called the Kamdotsev-Petviashvili (KP) and the Davey-Stewartson (DS) equations. An important advantage of the inverse spectral method as compared to standard PDE techniques is that it provides an efficient way to study the long-time behaviour of the solution. For equations in one-space dimension, such as KdV and NLS< it can be shown that the solution is dominated by N-solitons. Although there exists generalisations of solitons for equations in two space variables, called lumps and dromions, their role in the asymptotic characterisation of the solution as t grows remains unknown. It is the goal of this project to investigate the long time behaviour of the solution of the KP and DS equations, to investigate the existence of coherent structures of these equations and to elucidate the role played by lumps and dromions in the long time asymptotics of the solutions.
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Organisation Website: http://www.imperial.ac.uk