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Shock waves in dispersive hydrodynamics: analytical theory and numerical simulations (Advert Reference: RDF19/EE/MPEE/EL)

  • Full or part time
  • Application Deadline
    Friday, January 25, 2019
  • Funded PhD Project (Students Worldwide)
    Funded PhD Project (Students Worldwide)

Project Description

Shock waves are ubiquitous nonlinear phenomena observed in nature. Thunder, the crack of a whip, and the boom heard from a jet plane surpassing the speed of sound are familiar occurrences in human experience and all result from the generation of viscous shock waves in air.

Dispersive shock waves (DSWs), the subject of this PhD project, are of a very different type, lacking dissipation and realized as expanding oscillatory disturbances in a dispersive medium. These DSWs have yielded novel dynamics and have recently attracted much attention in connection with ground breaking experiments on superfluids and optical media. One of the reasons for this interest is that the study of DSW behaviour could greatly help in the understanding of the properties of the medium through which they propagate. Physical examples of DSWs range from undular bores observed in shoaling tsunami propagation to nonlinear diffraction patterns due to light propagation in optical crystals.

The project will explore DSWs in systems described by nonlinear partial differential equations modelling wave propagation in fluids and optical media for some special cases not covered by the existing theory. The mathematics involved will include exact and asymptotic methods such as inverse scattering transform Whitham modulation theory and matched asymptotic expansions. The developed analytical theory will be supported by direct numerical simulations so familiarity with numerical techniques for PDEs is essential. The project could also involve comparisons with the data obtained in physical experiments.

The principal supervisor for this project is Gennady El.

Eligibility and How to Apply:

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. RDF19/EE/MPEE/EL) will not be considered.

Deadline for applications: Friday 25 January 2019
Start Date: 1 October 2019

Northumbria University is an equal opportunities provider and in welcoming applications for studentships from all sectors of the community we strongly encourage applications from women and under-represented groups.

Funding Notes

The studentship is available to Students Worldwide, and covers full fees and a full stipend, paid for three years at RCUK rates (for 2018/19, this is £14,777 pa).


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 Hoefer, M.A. Dispersive shock waves and modulation theory, Physica D 333 (2016) 11 – 65

3. Maiden, M.D., Anderson, D.V., Franco, N.A., El, G.A. and Hoefer, M.A., Solitonic dispersive hydrodynamics: theory and observation, Phys. Rev. Lett. 120 (2018) 144101.

4. Congy, T., El, G.A., Hoefer, M.A., and Shearer, M., Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure, arxiv pre-print (2018),

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