Emergent phenomena in nonlinear dispersive waves
PDW
22 July 2024 to 16 August 2024
Programme theme
Emergence is a powerful concept that plays a fundamental role in many areas of modern mathematics and physics. In a system composed of a very large number of elementary constituents, e.g. classical or quantum particles, even with simple laws of interaction, the observed macroscopic behaviour can be highly nontrivial. This coarse-graining from microscopic to macroscopic scales is at the heart of hydrodynamic theories for inhomogeneous, dynamic many-body systems. These theories, that include classical fluid mechanics, describe various, sometimes exotic, systems and phenomena such as the non-equilibrium dynamics of Bose-Einstein condensates and electron flows in graphene. A very different kind of hydrodynamics arises when the microscopic system's constituents are waves. The subject of dispersive hydrodynamics—the theory of multiscale phenomena in nonlinear dispersive waves—has attracted much attention recently and was the focus of the 6-month HYD2 programme “Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves” at the Isaac Newton Institute in July-December 2022. This 4-week satellite programme aims to capitalise on the newfound collaborations and scientific problems that emerged over the course of the HYD2 programme.
This satellite programme is organised around three synergistic themes:
1. Emergent hydrodynamics of nonlinear dispersive waves in integrable and nonintegrable systems, numerical simulation, and physical applications
- Recent advances in modulation theory and dispersive shock waves
- Multidimensional dispersive hydrodynamics
- Boundary value problems in nonlinear dispersive waves
- Inverse scattering transform (IST) and asymptotic Riemann-Hilbert problem techniques
- Numerical approaches to multiscale nonlinear wave phenomena
- Applications in geophysical fluid dynamics, nonlinear optics and condensed matter physics
2. Stability of nonlinear dispersive waves and emergent phenomena in unstable wave systems
- Rigorous stability analysis of nonlinear dispersive waves in integrable and non-integrable systems
- Modulational instability and rogue wave formation as emergent phenomena
- Physical applications
3. Soliton gases, generalised hydrodynamics and statistical mechanics of integrable systems
- Integrable systems with random initial data
- Random matrix theory and statistical mechanics of integrable systems
- Spectral theory of soliton gases
- GHD-soliton gas connections
- Physical applications of integrable turbulence and soliton gases
Organisers
- Magda Carr Newcastle University
- Gennady El Northumbria University
- Mark Hoefer University of Colorado Boulder
- Antonio Moro Northumbria University
- Barbara Prinari University at Buffalo
- Matteo Sommacal Northumbria University
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