Mathematical Sciences

Research

Linear and nonlinear waves

The group's interests are in wave motion in a variety of physical situations, including geophysical fluid dynamics, water waves, solid mechanics, Bose-Einstein condensates, electromagnetism and acoustics. The group develop and apply exact, numerical, asymptotic and perturbation techniques to pursue research on linear and nonlinear waves, with a focus on solitary waves and soliton theory, stochastic wave systems, wave generation, and diffraction and scattering by obstacles.

Academic staff within this research group:

  • Dr Gennady El: Singular limits of nonlinear dispersive waves; Whitham theory; solitons and dispersive shock waves/undular bores in integrable and non-integrable systems; nonlinear dynamics of Bose-Einstein condensates; kinetic equations for solitons.
  • Professor Roger Grimshaw: Nonlinear waves, with an emphasis on geophysical fluid dynamics, theoretical oceanography and dynamical meteorology. There is a particular interest in solitons and soliton equations, internal solitary waves in the ocean and atmosphere, vortices and ocean eddies, and related topics. The mathematics involved is pertubation techniques and asymptotic analyses of partial differential equations, combined with numerical simulations.
  • Dr Karima Khusnutdinova: Waves in inhomogeneous media and complex systems (fluid and solid mechanics, mechanics of multiphase flows, geophysical applications), with an emphasis on nonlinear waves and their interactions, scattering and instabilities.
  • Professor Chris Linton: Multiple scattering in acoustics and linear water wave theory; Interaction of waves with large arrays; Water-wave/sea-ice interaction; Edge waves and trapped modes; Efficient computation of Green's functions and lattice sums.
  • Dr Emiliano Renzi: Theory and applications of water waves: wave energy extraction, tsunami generation and propagation, wave-structure interaction, coastal flooding. Analytic methods in Engineering , including partial differential equations, special functions (Laguerre, Bessel, Chebyshev, etc.) and perturbation techniques. 

Research students: