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Integrable turbulence and statistical mechanics of nonlinear dispersive waves (Advert Reference: RDF20/EE/MPEE/EL)

  • Full or part time
  • Application Deadline
    Friday, January 24, 2020
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

Turbulence is one of the most recognizable, and at the same time, one of the most intriguing forms of nonlinear motion that is commonly observed in everyday phenomena such as wind blasts or fast flowing rivers. Despite its widespread occurrence, the mathematical description of turbulence remains one of the most challenging problems of modern science. Physical mechanisms giving rise to turbulent motion can be very different but typically they involve some sort of dissipation, e.g. viscosity.

The proposed project will explore a very different kind of turbulence that does not involve any dissipation but is concerned with dynamics and statistics of random nonlinear waves that are modelled by the so-called integrable partial differential equations (PDEs). These equations often represent universal mathematical models describing nonlinear wave phenomena in water waves, optical media and superfluids.

Solitons are localized solutions of integrable wave equations that can be viewed as “particles’’ of complex statistical objects called soliton gases. These “integrable’’ gases present fundamental interest for applications, in particular, in connection with the appearance of extreme waves in the ocean or in optical fibres. Additionally, recent analytical and numerical studies of integrable turbulence revealed a number of intriguing connections between dynamics of classical soliton gases and statistical mechanics of quantum many-body systems.

In the project, integrable turbulence and soliton gases will be studied analytically and numerically in the framework of several integrable PDE models describing nonlinear wave propagation in fluids and nonlinear optical media.

The successful candidate is an applied mathematician or theoretical physicist with strong analytical and programming skills. Solid background in asymptotic methods, PDEs and nonlinear waves is essential. Some knowledge in statistical physics is desirable. Throughout the development of the project, the candidate is expected to interact with an international, multidisciplinary team of researchers and present results at national and international conferences.

The principal supervisor for this project will be Professor Gennady El. The second supervisor will be Dr Antonio Moro.

Please note eligibility requirement:
• Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
• Appropriate IELTS score, if required.
• Applicants cannot apply for this funding if currently engaged in Doctoral study at Northumbria or elsewhere.

For further details of how to apply, entry requirements and the application form, see

Please note: Applications that do not include a research proposal of approximately 1,000 words (not a copy of the advert), or that do not include the advert reference (e.g. RDF20/EE/MPEE/EL) will not be considered.

Deadline for applications: 24 January 2020

Start Date: 1 October 2020

Northumbria University takes pride in, and values, the quality and diversity of our staff. We welcome applications from all members of the community. The University holds an Athena SWAN Bronze award in recognition of our commitment to improving employment practices for the advancement of gender equality.

Funding Notes

The studentship is available to Home/EU/Worldwide students where a full stipend, paid for three years at RCUK rates (for 2019/20, this is £15,009 pa) and full fees.


1. Biondini, G., El, G.A., Hoefer, M. and Miller, P.D., Dispersive hydrodynamics: Preface, Physica D 333 (2016) 1-5
2. El, G.A. and Kamchatnov, A.M., Kinetic equation for a dense soliton gas, Phys. Rev. Lett. 95 (2005) Art No 204101
3. Roberti, G., El, G., Randoux, S., and Suret, P., Early stage of integrable turbulence in the one-dimensional nonlinear Schrödinger equation: A semiclassical approach to statistics Phys. Rev. E, 100 (2019) 032212
4. El, G.A., Khamis, E.G. and Tovbis, A., Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves, Nonlinearity 29 (2016) 2798 – 2836.

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