Integrable systems and applications

Workshop theme

The workshop will bring an in-depth focus on analytical methods used in the study of dispersive shock waves (DSW) and related phenomena in dispersive systems.  Several areas of current interest will be covered:

(i) The development of the inverse scattering transform (IST) and the Riemann-Hilbert approach to semi-classical limits for integrable partial differential equations (PDEs) with non-zero initial boundary conditions.

(ii) Analysis of perturbed periodic waves in dispersive systems with connections to rigorous modulation theory, dynamics, and stability.

(iii) Multidimensional dispersionless systems, their dispersive deformations, and dispersive regularisation of multidimensional wavebreaking.

(iv) Rigorous dispersive hydrodynamic research in connection with other programme themes including numerical analysis of dispersive systems and relationships to conservation law theory.

This workshop will take place at Loughborough University. For more information and to register, please click here

Invited Speakers:

• Deniz Bilman (University of Cincinnaty, US), On universal wave patterns in rogue wave formation
• Gino Biondini (University at Buffalo, US), On one-dimensional reductions and integrability of the Whitham equations for the Kadomtsev- Petviashvili equation
• Jerry Bona (University of Illinois Chicago, US), KdV in a quarter plane: asymptotic periodicity and mass transport
• Sonia Boscolo (Aston University, UK), Control of complex nonlinear wave dynamics in dispersive systems by machine learning
• Roberto Camassa (University of North Carolina, US), Some issues in the mathematical modeling of internal wave propagation
• Maciej Dunajski (University of Cambridge, UK), Elizabethan vortices 
• Gennady El (Northumbria University, UK), Generalised Riemann problem for soliton gas
• Sergey Gavrilyuk (Aix-Marseille University, France), Soliton limit for the Whitham modulation equations for the BBM equation
• Mark Hoefer (University of Colorado Boulder, US), Modulated multiphase waves in soliton - mean flow interaction
• Rossen Ivanov (Technological University Dublin, Ireland), Integrable systems on symmetric spaces
• Robert Jenkins (University of Central Florida, US), Connecting different models of soliton gases
• Christian Klein (University of Burgundy, France), Numerical study of Davey-Stewartson systems
• Yuji Kodama (Ohio State University, US), KP solitons and algebraic curves
• Boris Konopelchenko (University of Salento, Italy), On the fine structure and hierarchy of gradient catastrophes for the multi-dimensional homogeneous Euler equation
• Boris Kruglikov (UiT The Arctic University of Norway), On geometry of higher dimensional dispersionless integrable equations
• Antonio Moro (Northumbria University, UK), Statistical ensembles, nonlinear differential equations and integrability: from mean field models to hydrodynamic chains
• Miguel Onorato (University of Turin, Italy), Thermalization vs integrability in the Fermi-Pasta-Ulam-Tsingou chain
• Lev Ostrovsky (University of Colorado Boulder, US), Joint effects of rotation and topography on internal solitary waves
• Alfred Osborne (Nonlinear Waves Research Corporation, Alexandria, VA, US) Two Fundamental Properties of Nonlinear Integrable Wave Equations with Hamiltonian Perturbations
• Emilian Parau (University of East Anglia, UK), A dissipative Nonlinear Schroedinger model for wave propagation in the marginal ice zone
• Barbara Prinari (University at Buffalo, US), Inverse Scattering Transform, solitons and soliton interactions for the complex coupled short-pulse equation
• Michael Shearer (North Carolina State University, US), The Dispersive Riemann Problem for the BBM Equation
• Matteo Sommacal (Northumbria University, UK) Integrability, instabilities, and the onset of rogue waves
• Alexander Tovbis (University of Central Florida, US), Recent developments in spectral theory of soliton gases for integrable equations 
• Raffaele Vitolo (University of Salento, Italy), Projective geometry of homogeneous second-order Hamiltonian operators
• Derchyi Wu (Academia Sinica, Taiwan), Stability of the Kadomtsev-Petviashvili multi-line solitons