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Extensions of the Alber equation and statistical modulation instability analysis for crossing seas

School of Science and Engineering

About the Project

It is well known that nonlinear dispersive equations exhibit modulation instability, a phenomenon linked to extreme events such as rogue waves. Modulation instability was first discovered as the linear instability of plane-wave solutions to nonlinear equations, but realistic problems demand a more flexible framework. In that context, the Alber equation was introduced as a stochastic moment system, providing a framework for the statistical analysis for the stability of a homogeneous wave-field. Alber equations have several novel features, and their rigorous study is only now reaching maturity, with several questions still open. Moreover the classical Alber equation only covers quasi-unidirectional problems, excluding in particular crossing seas (wave systems arriving to the same area from different directions), which have recently been identified as crucial settings for the appearance of rogue waves. In this project an extended two-dimensional Alber equation, including crossing seas, will be derived and studied.

For informal enquiries about the project, contact Dr Agissilaos Athanassoulis ()
For general enquiries about the University of Dundee, contact

Applicants must have obtained, or expect to obtain, a first or 2.1 UK honours degree, or equivalent for degrees obtained outside the UK in a relevant discipline.

English language requirement: IELTS (Academic) score must be at least 6.5 (with not less than 5.5 in each of the four components). Other, equivalent qualifications will be accepted. Full details of the University’s English language requirements are available online:


Step 1: Email Dr Agissilaos Athanassoulis () to (1) send a copy of your CV and (2) discuss your potential application and any practicalities (e.g. suitable start date).

Step 2: After discussion with Dr Athanassoulis, formal applications can be made via UCAS Postgraduate. When applying, please follow the instructions below:

Apply for the Doctor of Philosophy (PhD) degree in Mathematics: Select the start date and study mode (full-time/part-time) agreed with the lead supervisor.

In the ‘provider questions’ section of the application form:
- Write the project title and ‘’ in the ‘if your application is in response to an advertisement’ box;
- Write the lead supervisor’s name and give brief details of your previous contact with them in the ‘previous contact with the University of Dundee’ box.

In the ‘personal statement’ section of the application form, outline your suitability for the project selected.

Funding Notes

There is no funding attached to this project. The successful applicant will be expected to provide the funding for tuition fees, project specific bench fees and living expenses via external sponsorship or self-funding


A. Athanassoulis, G. Athanassoulis, M. Ptashnyk & T. Sapsis, "Strong solutions for the Alber equation and stability of unidirectional wave spectra", to appear in Kinetic & Related Models (2020)

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