Integrable systems of hydrodynamic type in 2+1 dimensions

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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).

References:
[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.

Funding:
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.

Entry requirements:
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 - http://www.lboro.ac.uk/international/applicants/english/

Contact details:
Name: Prof Evgeny Ferapontov
Email address: [Email Address Removed]
Telephone number: +44(0)1509 223309

How to apply:
All applications should be made online at http://www.lboro.ac.uk/study/apply/research/.
Under programme name, select Mathematical Sciences and please quote reference number: MA/EVF-1/2017

Supervisors:
Primary supervisor: Prof Evgeny Ferapontov