EPSRC Reference: 
EP/H04261X/1 
Title: 
Integrability in Multidimensions and Boundary Value Problems 
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: 
01 June 2011 
Ends: 
31 May 2015 
Value (£): 
465,254

EPSRC Research Topic Classifications: 
Mathematical Analysis 
Nonlinear Systems Mathematics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
There exist certain distinctive nonlinear equations called integrable. The impact of the mathematical analysis of such special equations cannot be overestimated. For example, firstly, for integrable equations we have learned detailed aspects of solution behaviour, which includes the longtime asymptotics of solutions and the central role played by solitons. Secondly, it has become apparent that some of the lessons taught by integrable equations have applicability even in nonintegrable situations. Indeed, many investigations in the last decade regarding wellposedness of PDEs in appropriate Sobolev spaces have their genesis in results coming from the theory of integrable systems, albeit in nonintegrable settings. Perhaps the two most important open problems in the theory of integrable equations have been (a) the solution of initialboundary as opposed to initial value problems and (b) the derivation and solution of integrable nonlinear PDEs in 3+1 dimensions. In the last 12 years, the PI has made significant progress towards the solution of both of these problems. Namely, regarding (a) he has introduced a unified approach for analysing boundary value problems in two dimensions and regarding (b) he has derived and solved integrable nonlinear PDEs in 4+2. However, many fundamental problems remain open. The proposal aims to investigate several such problems among which the most significant are: (a) the extension of the method for solving boundary value problems from two to three dimensions and (b) the reduction of the new integrable PDEs from 4+2 to 3+1. In addition, the CamassaHolm analogue of the celebrated sine Gordon equation, several boundary value problems of the elliptic version of the Ernst equation, and the KdV equation on the halfline with time periodic boundary conditions will also be investigated.

Key Findings 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Potential use in nonacademic 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.cam.ac.uk 