School of Mathematics, Tel: +44 (0) 1509 22 2861

Linear and nonlinear waves research group

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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.

We have web sites for the EPSRC projects entitled Mathematical Methods for Wave Interaction with Large Arrays and Mathematical Modelling of Nonlinear Waves in Layered Elastic Waveguides with Inhomogeneities.

The group holds seminars in the Applied Mathematics series.


Academic staff

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 Maureen McIver The interaction of water waves and structures. Uniqueness problems in water waves and acoustics, in particular the existence of trapped modes at frequencies that are embedded in the continuous spectrum.
Professor Phil McIver The interaction of water, acoustic and elastic waves with structures including the following: scattering, radiation and sloshing problems; trapped modes in water waves; large arrays; initial-value problems.

Research associate

Dr Victor Zalipaev Zalipaev Semiclassical analysis of quantum electonic resonators in magnetic field, 2D electronic gas transport through quantum waveguide-resonator mesoscopic systems and graphene structures. Mathematical theory of diffraction and propagation of acoustic, electromagnetic and elastic waves. Asymptotic methods for PDE (WKB, ray and Maslov canonical operator methods, GTD, matched asymptotic techniques and boundary layer methods).

Research students

Azwani Alias blank Mathematical modelling of internal solitary waves.
Ben Carter Very large floating structures. The method of matched asymptotic expansions.
Richard Clift blank Generation, propagation and interaction of internal undular bores. Inverse spectral transform and Whitham's theory of slow modulations.
Kieron Moore Nonlinear waves in layered elastic waveguides.
Wei King Tiong Nonlinear waves in geophysical fluid dynamics: numerical and analytical study of modulated periodic wavetrains in variable media using the Whitham method.
Nikolas Tymis Analytical techniques for acoustic scattering by arrays of isotropic point scatterers.
Xizheng Zhang blank Internal waves in inhomogeneous oceanic waveguides.
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