Integrable systems of hydrodynamic type in 2+1 dimensions PhD

Mathematical Sciences
Entry requirements:
2:1 +
Not available
Reference number:
UK/EU fees:
International fees:
Application deadline:
01 September 2018



of research classed as 'internationally recognised'

REF 2014


in the UK for Mathematics

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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

Systems of hydrodynamic type occur in a wide range of applications in various areas of pure and applied mathematics. In 2+1 dimensions, there exists an efficient approach to the classification of integrable systems of this kind based on the method of hydrodynamic reductions [1]. In the two-component case, the classification of integrable systems of hydrodynamic type was proposed in [2]. The goal of this project is to extend the approach of [2] to the case of three-component systems. The advantage of the multi-component case is the existence of a simple necessary condition for integrability based on the Haantjes tensor [3].

The project will require basic knowledge of differential equations, differential geometry, and familiarity with symbolic computations (Mathematica/Maple). 


  1. E.V. Ferapontov and K.R. Khusnutdinova, On integrability of (2+1)-dimensional quasilinear systems, Comm. Math. Phys. 248 (2004) 187-206.
  2. E.V. Ferapontov and K.R. Khusnutdinova, The characterization of 2-component (2+1)-dimensional integrable systems of hydrodynamic type, J. Phys. A: Math. Gen. 37, no. 8 (2004) 2949-2963.
  3. E.V. Ferapontov and K.R. Khusnutdinova, Double waves in multi-dimensional systems of hydrodynamic type: the necessary condition for integrability, Proc. Royal Soc. A 462 (2006) 1197-1219.


Primary supervisor:  Prof Evgeny Ferapontov

Find out more

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics.

A relevant Master's degree and / or experience in one or more of the following will be an advantage:
Differential Equations; Differential Geometry; Computer Algebra (Mathematica/Maple).

All students must also meet the minimum English Language requirements.

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 is an open call for candidates who are sponsored or who have their own funding. If you do not have funding, you may still apply, however Institutional funding is not guaranteed. Outstanding candidates (UK/EU/International) without funding will be considered for funding opportunities which may become available in the School.

How to apply

All applications should be made online. Under programme name select Mathematical Sciences. Please quote reference number: MA/EVF-1/2017