Multidimensional integrable systems: deformations of dispersionless limits PhD

Mathematical Sciences
Entry requirements:
3 years
not available
Reference number:
Start date:
01 October 2018
Is funding available?
UK/EU fees:
International fees:
Application deadline:
16 February 2018



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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. 

Project detail

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.

The Department of Mathematical Sciences works to deliver innovative research that has the potential to have significant impact on industry. 

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.


Primary supervisor: Dr. Vladimir Novikov

Find out more

For further project details email Dr. Vladimir Novikov or register your interest and ask us a question.

To find out more about postgraduate research in the School of Science please visit our website.

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.

Applicants must meet the minimum English Language requirements, details available on the website.

Fees and funding


Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Special arrangements are made for payments by part-time students.

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.

How to apply

All applications should be made online. Under programme name, select ‘Mathematics’.

Please quote reference number: VN/MA/2018

Application details

Reference number:  VN/MA/2018
Start date: 01 October 2018
Application deadline: 16 February 2018