| Universality of Nonlinear Behaviour |
| Organizers: |
Peter Clarkson (University of Kent, U. K.) |
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In this minisymposium, the focus will be the study of nonlinear equations, in particular integrable systems. The modern theory of integrable systems and the modern theory of nonlinear waves are intimately related topics, with the Korteweg-de Vries, nonlinear Schrödinger and Boussinesq equations, being the prototypical examples.
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The Painlevé equations, discovered about a hundred years ago, are special amongst nonlinear ordinary differential equations in that they are integrable?due to their representation as Riemann- Hilbert problems. The Painlevé equations also arise as symmetry reductions of nonlinear waves equations such as the Korteweg-de Vries, nonlinear Schrödinger and Boussinesq equations. Further they are nonlinear analogues of the classical special functions with a plethora of remarkable properties.
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The minisymposium will be focus on some of the recent developments in the research on integrable models which are deeply connected to the theory of nonlinear waves.
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| List of Speakers: |
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| 1)Robert Buckingham ( University of Cincinnati, U. S. A. ) |
| "Applications of Painlevé Functions to Nonlinear Wave Equations
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| 2) Peter Clarkson ( University of Kent, U.K. ) |
| "Painlevé equations - nonlinear special functions" |
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| 3) Tamara Grava ( SISSA, Trieste, Italy ) |
| "Solution of the generalized nonlinear Schrödinger equation in the semiclassical limit and Painlevé equations" |
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| 4) Thomas Kecker ( University College London, U. K. ) |
| "Solutions of ODEs with movable algebraic singularities" |
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| 5) Timothy Marchant ( University of Wollongong, Australia ) |
| "Solitary waves and dispersive shock waves in colloidal media" |
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| 6) Alexander Mikhailov ( University of Leeds, U. K. ) |
| "Wave fronts and soliton webs--exact solutions of the 2D
Volterra system" |
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| 7) Peter Miller ( University of Michigan, U. S. A. ) |
| "Asymptotics of Rational Solutions of the Inhomogeneous Painlevé-II Equations" |
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| 8) Sheehan Olver ( University of Sydney, Australia ) |
| "Numerical calculation of finite random matrix statistics, and the onset of universality" |
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| 9) Jani Virtanen ( University of Reading, U. K. ) |
| "Riemann-Hilbert problems in Hardy spaces" |
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