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

University of Dundee

School of Science and Engineering

Project Description

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 ([email protected])

For general enquiries about the University of Dundee, contact [email protected]

Funding Information

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.

Eligibility Requirements

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

Application Process

Step 1: Email Dr Agissilaos Athanassoulis ([email protected]) 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 our direct application system. When applying, please follow the instructions below:

Apply for the Doctor of Philosophy (PhD) degree in Mathematics: Mathematics : Study : University of Dundee

Please select the study mode (full-time/part-time) and start date agreed with the lead supervisor.

In the Research Proposal section, please:

  • Enter the lead supervisor’s name in the ‘proposed supervisor’ box
  • Enter the project title listed at the top of this page in the ‘proposed project title’ box

In the ‘personal statement’ section, please outline your suitability for the project selected.

Supplementary Information

Our research community thrives on the diversity of students and staff which helps to make the University of Dundee a UK university of choice for postgraduate research. We welcome applications from all talented individuals and are committed to widening access to those who have the ability and potential to benefit from higher education.


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)

To apply for this PhD, please email a.athanassoulis@dundee.ac.uk.

Before sending your email, please double check you have followed all guidelines in this listing and have included a reference number if asked to do so.