Left: Solitary wave transmission through a dispersive shock wave in a viscous fluid conduit, Boulder, CO, USA © Mark Hoefer, 2016.
Right: Undular bore on the Severn river near Gloucester, UK © Mark Humpage, 2007.
Dispersive hydrodynamics has emerged as a unified mathematical framework for the description of multiscale nonlinear wave phenomena in dispersive media, encompassing both dynamic and stochastic aspects of wave propagation. Recent theoretical and experimental developments have opened up new areas for research, with intriguing open issues in both theory and applications. These include the understanding of fundamental regularisation mechanisms of hydrodynamic singularities via the generation of dispersive shock waves (DSWs) and related phenomena. Physical examples of dispersive hydrodynamic phenomena include undular bores on rivers, in the ocean and atmosphere, nonlinear diffraction patterns in optics and quantum fluids, turbulence in fibre lasers and superfluids.
The mathematical programme weaves together research topics on integrable and nonintegrable dispersive partial differential equations, hyperbolic conservation laws, convex and nonconvex dispersive hydrodynamic systems. Numerous physical applications of dispersive hydrodynamics in geophysics, nonlinear optics, superfluids and magnetic materials will be explored. The programme is designed to encourage interactions amongst mathematicians, physicists, and engineers specialising in the analysis of dispersive systems, experiments and numerical simulations. Special emphasis is given to involving young researchers and to diversity among the participants.
The programme is organized around four overlapping themes:
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The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
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