EPSRC Reference: 
EP/H022201/1 
Title: 
Integrable Nonlinear Evolution PDEs on the Interval 
Principal Investigator: 
Fokas, Professor A 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Applied Maths and Theoretical Physics 
Organisation: 
University of Cambridge 
Scheme: 
Standard Research 
Starts: 
18 January 2010 
Ends: 
17 April 2010 
Value (£): 
15,982

EPSRC Research Topic Classifications: 
Nonlinear Systems Mathematics 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
During the threemonth research visit of Professor Deconinck to Cambridge, we will investigate two problems which arise in the analysis of the celebrated nonlinear Schr\ odinger equation (NLS) formulated on a finite interval: (a) The reduction of the general theory for solving intialboundary value problems on the finite interval in the particular case that the boundary values are periodic in space. (b) The asymptotic behaviour of the solution in the case that the given Dirichlet boundary conditions are periodic in time. Regarding the first problem, we note that the related beautiful algebraicgeometric theory characterises the particular finitegap case in terms of theta functions. Our goal is to characterise the general case in terms of a matrix RiemannHilbert problem and to rederive the results of the finitegap representation as a particular case. Regarding the second problem, we note that for the linearized version of the NLS it has been shown recently that the asymptotic behaviour of the solution depends on the commensurability of the time period $T$ of the boundary data with $L^2/ \pi$, where $L$ is the length of the finite interval. Our goal is to obtain an analogous result for the NLS.

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Organisation Website: 
http://www.cam.ac.uk 