Details of Grant 

EPSRC Reference:	EP/C527747/1
Title:	Multidimensional integrable systems, differential-difference equations and the symmetry approach
Principal Investigator:	Novikov, Dr V
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Maths Statistics & Actuarial Sci
Organisation:	University of Kent
Scheme:	Postdoc Res Fellowship PreFEC
Starts:	01 March 2006	Ends:	31 July 2007	Value (£):	116,792
EPSRC Research Topic Classifications:	Mathematical Physics Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 14 Feb 2005 PDF Mathematical Sciences Sift 2004/05 Deferred
Summary on Grant Application Form
Integrable partial differential equations are of great interest in modern mathematics, where they have important connections with algebra and differential geometry, and in physics, where they describe many important physical models. Many concepts of modern mathematical physics such as solitons, instantons and quantum groups have their origin in theory of integrable systems.One of the most important and challenging problems in the theory of integrable systems is how to recognize when a given equation is integrable. This project is devoted to multidimensional and differential-difference polynomial integrable systems. The combination of the Perturbative Symmetry Approach and number theoretical methods is proposed for studying integrability of multidimensional and differential-difference equations as well as for obtaining complete classification results of integrable systems of this type.The aims of the proposed research are the following:I. Obtain a global (at arbitrary order) classification of integrable scalar and coupled polynomial homogeneous equations in 2+1 dimensions. II. Extend the perturbative symmetry approach to higher dimensional partial differential equations.III. Extend the symbolic method to differential-difference equations.IV. Obtain a global classification of integrable scalar and coupled differential-difference equations.AMS 2000 subject classification: 37K1 0, 37K35
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Organisation Website:	http://www.kent.ac.uk