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.

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:

  • 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.