Nonlinear waves arise throughout physics whenever wave amplitudes become sufficiently large that linear approximations break down. Understanding their behaviour remains one of the central challenges of modern physics. While nonlinear waves in continuous media have been extensively studied, many natural and engineered systems are inherently discrete and structured as networks. Examples include signal propagation in neural brain networks, transport and flow in circulatory and pipe systems, wave transmission in engineered lattices and metamaterials, and the spreading of information or activity across social networks.
The project will focus on nonlinear wave models defined on graphs and discrete networks. Possible systems include discrete versions of the nonlinear Schrödinger equation, Klein–Gordon and Duffing-type models, and intrinsically discrete systems such as the Fermi–Pasta–Ulam–Tsingou model. The main objective will be to understand how nonlinear wave phenomena—such as localisation, coherence, instability, synchronisation, and transport—depend on the underlying graph structure, including its connectivity, symmetries, topology, and spectral characteristics.
This research is highly interdisciplinary and combines ideas from nonlinear dynamics, Hamiltonian and Lagrangian systems, statistical mechanics, graph theory, spectral theory, machine learning, and differential equations. The project will involve substantial theoretical and computational work, including large-scale numerical simulations and scientific programming. Scientific machine learning techniques may also be employed to identify hidden structures, coherent patterns, and reduced-order representations of nonlinear wave dynamics on complex graphs.
At the same time, the nonlinear wave models investigated in the project may themselves be extended and adapted to describe neural-network architectures and information propagation in biologically inspired or artificial learning systems. This creates exciting opportunities to explore the interplay between nonlinear physics, network dynamics, and artificial intelligence methodologies.
Depending on the direction of the research, opportunities may arise for collaborations with interdisciplinary groups working on complex systems, neuroscience, machine learning, and discrete physical systems.
By joining Dr Proment’s research group, you will become part of a vibrant and internationally oriented research environment with expertise in nonlinear physics, quantum fluids, and computational physics. You will develop advanced analytical, computational, and research skills while working on fundamental scientific problems with broad applications across physics, mathematics, and data-driven sciences.
Entry Requirements
The entry requirements are a 2:1 Bachelor's and a Master's in Physics (or equivalent, for example Mathematics, Natural Sciences, Computer Sciences).
Mode of Study
Full or Part time
Start Date
1 October 2026
