PhD Studentship: Multidimensional Integrable Systems: Deformations of Dispersionless Limits

Loughborough University

Start date of studentship: 1st October 2018

Closing date for applications: 16th February 2018


Primary supervisor: Vladimir Novikov

Integrable multidimensional PDEs appear in many areas of modern Mathematics and Nonlinear Science as universal models. Recently there has been significant progress in understanding and developing the integrability theory of 3-dimensional first order quasilinear systems, led by the Loughborough team. Such systems appear in a wide range of applications, including shallow wave theory, general relativity, differential geometry. Moreover, the further novel approach to the integrability of multidimensional soliton equations was proposed by the team in Loughborough, based on the method of dispersive deformations of hydrodynamic reductions – the method of deformed hydrodynamic reductions. The ultimate goal of the project is to obtain the complete description of integrable dispersive multidimensional systems. This project relates to the interconnection of Integrable Systems and Differential Geometry.

Loughborough University is a top-ten rated university in England for research intensity (REF2014). In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career.

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Full Project Detail:

Integrable multidimensional PDEs appear in many areas of modern Mathematics and Nonlinear Science as universal models. There is the rich theory of integrable systems in 2-dimensions, while the theory of integrability in dimensions higher than 2 remains much less developed. Moreover, one distinguishes two types of integrable systems in higher dimensional case: dispersionless and dispersive integrable systems. Our team in Loughborough proposed a novel technique of studying integrability in higher dimensional case, which extends the definition of integrability in dispersionless case to fully dispersive systems – the method of deformed hydrodynamic reductions. This project will apply the method of deformed hydrodynamic reductions to multi-component systems of Davey-Stewartson type.

The method of deformed hydrodynamic reductions is also applicable to differential-difference and fully discrete discrete systems. The discrete systems of Davey-Stewartson type will also be studied.

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Entry requirements:

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematical Sciences or a related subject. A relevant Master’s degree and/or experience in one or more of the following will be an advantage: pure mathematics, differential geometry, integrable systems.

Funding information:

This studentship will be awarded on a competitive basis to applicants who have applied to this project and/or any of the advertised projects prioritised for funding by the School of Science.

The 3-year studentship provides a tax-free stipend of £14,553 (2017 rate) per annum (in line with the standard research council rates) for the duration of the studentship plus tuition fees at the UK/EU rate. International (non-EU) students may apply however the total value of the studentship will be used towards the cost of the International tuition fee in the first instance.

Contact details:

Name: Dr. Vladimir Novikov


Tel: +44 1509 223305

How to apply:

Applications should be made online at Under programme name, select Mathematics

Please quote reference number: VN/MA/2018

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