Linear and nonlinear waves

Image of the Peregrine breather (a model for rogue waves) was created by K.Khusnutdinova [Loughborough]

The group's interests are in developing new analytical and numerical approaches in order to understand and predict wave motion in a variety of physical situations, with a focus on nonlinear waves, wave generation, interactions, instabilities, and diffraction and scattering by obstacles.

Typical applications include tsunamis and other water waves, internal waves and geophysical fluid dynamics, strain waves in solids, acoustics and electromagnetic waves. There are significant links to integrable systems and engineering experiments and applications.

Applied maths seminar schedule

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The Linear and Nonlinear Waves research group leads the Special Interest Group on “Mathematical Challenges of Nonlinear Waves and Interfacial Dynamics” funded by the UK Fluids Network, in partnership with Bath and Imperial. The SIG has organised 5 workshops, of which 3 in Loughborough, involving more than 50 researchers in the field, from early career researchers to international leading experts and industrial partners.

Karima Khusnutdinova and Sara Lombardo were part of the organising committee of the 4th IMA conference on Nonlinearity and Coherent Structures in 2021.

Karima Khusnutdinova is part of the organising committee for the British Applied Mathematics Colloquium (BAMC), the main annual UK conference in Applied Mathematics, which will be held in Loughborough in 2022.

Sample of recent publications:

R. Barros, W. Choi, P.A. Milewski (2020). Strongly nonlinear effects on internal solitary waves in three-layer flows, Journal of Fluid Mechanics 883, A16.
A. Degasperis, S. Lombardo, M. Sommacal (2019). Rogue wave type solutions and spectra of coupled nonlinear Schroedinger equations, Fluids 4, 57.
S. Michele and E. Renzi (2019). Effects of the sound speed vertical profile on the evolution of hydroacoustic waves, Journal of Fluid Mechanics 883, A28.
M.G. Blyth, D. Tseluiko, T.S. Lin, S. Kalliadasis (2018). Two-dimensional pulse dynamics and the formation of bound states on electrified falling films, Journal of Fluid Mechanics 855, 210-235.
C.M. Linton and I. Thompson (2018). Elastic Waves Trapped above a Cylindrical Cavity, SIAM Journal of Applied Mathematics 78, 2083-2104.
J. Eckhardt (2017). The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data, Archive for Rational Mechanics and Analysis 224, 21-52.
K.R. Khusnutdinova and X. Zhang (2016). Long ring waves in a stratified fluid over a shear flow, Journal of Fluid Mechanics 794, 17-44.

Dr Ricardo Barros

Nonlinear waves. Large Amplitude Internal waves in Stratified Fluids. Stability of Stratified Shear Flows.

Dr. Jonathan Eckhardt

Direct and Inverse Spectral Theory. Inverse Scattering Transform for Integrable PDEs. Long-time Asymptotics and Nonlinear Waves.

Dr. Karima Khusnutdinova

Fluid and Solid Mechanics. Nonlinear Waves. Applied Integrable Systems.

Prof. Chris Linton

Mathematical Techniques for Wave Diffraction by Obstacles. Wave Diffraction for Water Waves, Acoustics, Elasticity, Electromagnetism, Quantum Physics.

Prof. Sara Lombardo

Integrable Systems. Automorphic Lie Algebras. Analysis of Integrable PDEs. Nonlinear Waves.

Dr. Emiliano Renzi

Water Waves’ Energy Extraction. Tsunamis. Wave-Structure Interactions. Coastal Flooding.

Dr. Dmitri Tseluiko

Nonlinear Waves and Interfacial Phenomena. Phase-Transitions and Singularities in Sheared Liquid Films. Interfacial Electrohydrodynamics.

Dr Curtis Hooper

Postdoctoral research associate on the "Undular bores generated by fracture: viscoelastic and geometric effects" project funded by EPSRC, supervised by Dr. Karima Khusnutdinova.

Investigating the evolution of undular bores in solid waveguides with variable and complex geometry.

Dr Alex Kyriakis

Domain decomposition methods for partial differential equations

Dr Priscila Leal da Silva

Postdoctoral research associate on "The onset of instabilities in PDE's from analysis to algebraic geometry" project funded by the Royal Society, supervised by Prof. Sara Lombardo.

Understanding how a system behaves in time after external perturbations, with applications to the occurrance of anomalous waves in the ocean and atmosphere.

Dr Juliet Ojiako

Postdoctoral research associate on the “PLACINGS” project funded by EPSRC, supervised by Dr. Emiliano Renzi.

Designing activities to demonstrate the breadth and importance of STEM research, to attract underrepresented groups to careers in STEM, and to facilitate stronger connections between schools and industry.

Mr. Liam Baddeley. Primary Supervisor: Dr. Ricardo Barros. Large amplitude internal waves in a two-layer fluid.
Mr. Matthieu Fauvel. Primary Supervisor: Dr. Dmitri Tseluiko. Matthieu analysis of the effect of electro-osmotic flow on liquid foam stability.
Mr. Mateeb Khan. Primary Supervisor: Dr. Emiliano Renzi. The flow through and around wave energy converters at large and small scales.
Mr Benjamin Martin. Primary Supervisor: Dr. Karima Khusnutdinova. Stability of surface and internal ring waves.
Mr. Korsarun Nirunwiroj. Primary Supervisor: Dr. Karima Khusnutdinova. Mathematical modelling of internal waves in rotating stratified fluids.
Mr. Nerijus Sidorovas. Primary Supervisor: Dr. Karima Khusnutdinova. Mathematical modelling of nonlinear ring waves of moderate amplitude in fluids.
Mr. Jacob Vizor. Primary Supervisors: Dr. Karima Khusnutdinova (Mathematical Modelling) and Dr Pablo Ruiz (Experiments, Wolfson School). Nonlinear strain waves in solid waveguides at very high strain rates.