2020 applicants
Postgraduate Research Opportunity

Multi-component integrable systems and Bose-Einstein condensates


Title: Multi-component integrable systems and Bose-Einstein condensates

Funding: Full time Home/EU fees and a stipend of £15,009 p.a. (terms & conditions)

Application deadline: 3 July 2019 (interviews for shortlisted candidates are scheduled to take place w/c 15 July 2019)

Start date: October 2019 (or soon as possible thereafter).

Duration: 3 years (full time)

Location: Colchester Campus

Based in: Department of Mathematical Sciences

This studentship is now closed. View our other opportunities.


The proposed project aims to build up a systematic theory of rational solutions of multi-component integrable systems (i.e. systems of coupled nonlinear partial differential equations (PDEs) integrable/solvable by Inverse Scattering Method).

More specifically, it has the following research objectives:

  • To develop spectral theory of Lax operators with multiple discrete eigenvalues. 
  • To develop multi-pole dressing method for Lax operators related to simple Lie algebras. To study and classify rational soliton solutions. 
  • To describe the infinite set of integrals of motion and the associated Hamiltonian structures. 
  • To study possible reductions of integrable systems with multiple discrete eigenvalues and their soliton/rational solutions. 

We will restrict ourselves in this project to integrable systems with linear and quadratic dispersion laws. As a main prototype, we will deal with Nonlinear Schrodinger systems related to symmetric spaces (known as Fordy-Kulish models).

The project lies in the broad area of Applied Mathematics and Mathematical Physics, including some interdisciplinary elements – it brings together ideas from Functional analysis and Spectral theory, Group theory (Lie groups and Lie algebras, symmetries) and Differential geometry (symmetric spaces).

Depending on the successful candidate’s profile, the emphasis can be either on the algebraic or analytic aspects of the theory (ideally on both).


The award consists of a full Home/EU fee waiver or equivalent fee discount for overseas students (further fee details), a doctoral stipend equivalent to the Research Councils UK National Minimum Doctoral Stipend (£15,009 in 2019-20), plus £2,500 training bursary via Proficio funding, which may be used to cover the cost of advanced skills training including conference attendance and travel.


At a minimum, the successful applicant will have a good honours degree (1st class or high 2:1, or equivalent GPA from non-UK universities) in (pure or applied) mathematics or theoretical physics. An MSc in a relevant subject is desirable (preference for Upper Merit or above).

The ideal candidate will have strong background in mathematics (differential equations, algebra, analysis and geometry) and theoretical physics, and good programming skills.

Knowledge in one or more of the following areas is desirable:

  • integrable systems
  • nonlinear waves and solitons
  • scattering theory and analysis of PDEs
  • group theory (Lie groups and Lie algebras)
  • differential geometry (symmetric spaces).

Working knowledge of Maple and Mathematica is desirable.

An IELTS score of 6.5 or above, or equivalent (if applicable).

How to apply

You can apply for this postgraduate research opportunity online.

On the online application please upload:

  • CV
  • Personal statement
  • Transcripts of any undergraduate or Masters programmes
  • One reference
  • Any piece of coursework you have done, containing research elements (e.g., dissertations, projects).

Instruction to applicants

When you apply online you will be prompted to fill out several boxes in the form:

  • For "Course title" please put "PhD Mathematics"
  • For "Proposed research topic or area of research" please put the title of this studentship (Multi-component integrable systems and Bose-Einstein condensates)
  • For "If you have contacted a potential supervisor..." please put the name of the lead supervisor (Dr Georgi Grahovski)

If you have any informal queries about this opportunity please email the lead supervisor, Dr Georgi Grahovski (gggrah@essex.ac.uk)