EPSRC Reference: 
EP/I038675/1 
Title: 
Structure of partial difference equations with continuous symmetries and conservation laws 
Principal Investigator: 
Mikhailov, Professor AV 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Applied Mathematics 
Organisation: 
University of Leeds 
Scheme: 
Standard Research 
Starts: 
09 January 2012 
Ends: 
08 October 2015 
Value (£): 
255,685

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Analysis 
Numerical Analysis 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
24 May 2011

Mathematics Prioritisation Panel Meeting May 2011

Announced


Summary on Grant Application Form 
This is a Mathematics proposal in the broad area of Integrable Systems with a focus on difference equations. Many natural phenomena have a discrete nature or can be modelled in terms of difference equations. Any simulation of a continuous phenomena on a digital computers requires an appropriate discretisation. Difference equations have a wide range of practical applications from Fundamental Physics to Engineering.
The theory of difference equations is considerably less developed than the classical theory of differential equations. Broadly speaking our research project aims to reduce the gap between them and to explore new features that are not available in the case of differential equations. A reformulation of the theory of difference equations in terms of difference algebra will enable us to use a variety of new methods and provide a rigorous framework. From the other side, nontrivial examples originated from the applied theory of difference equations could serve as a basis for further development and new concepts in difference algebra.
It is difficult to overestimate the importance of continuous symmetries and local conservation laws in the theory and applications of differential equations. Often they carry the most valuable information about the model and are more important than exact solutions. In the project we will find a sequence of necessary conditions for the existence of a
high order symmetry (or a conservation law) for a given system of difference equations. Continuous symmetries and conservation laws can serve as a characteristic property for the class of integrable systems. Symmetries of
integrable partial differential equations can be generated by recursion (or Lenard) operators. We propose to develop an interesting and rather nontrivial extended analogue of Lenard's scheme.
Together with solutions of clearly set problems our project is poised to invade an uncharted territory of difference equations with approximate symmetries. To study properties and algebraic structures associated with approximately integrable equations will be a new and challenging direction of research.

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.leeds.ac.uk 