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Details of Grant 

EPSRC Reference: GR/N63062/01
Title: BOUNDARY VALUE PROBLEMS IN TWO AND THREE DIMENSIONS FOR INTEGRABLE 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: 30 January 2001 Ends: 29 July 2001 Value (£): 7,800
EPSRC Research Topic Classifications:
Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:
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Summary on Grant Application Form
The PI has recently introduced a new method for solving initial boundary value problems for linear and for integrable nonlinear PDEs. In a joint work with the VF this method has been applied to the solution of a general linear dispersive equation and to the NLS equation on the half line. These results will be extended to the case that the domain involves a time-dependent contour. Also, this method will be used to investigate a general class of boundary value problems for the Laplace and for the modified Helmholtz equations in a general regular polygon. The PI and the VF have collaborated closely on the rigorous investigation of the initial value problem for decaying initial data for integrable nonlinear PDES in three dimensions. They will now investigate initial value problems for such equations in the background of 1-line soliton.
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Organisation Website: http://www.imperial.ac.uk