Integrable Systems Group
The University of Sydney2017 Integrable Systems Workshop
The area of integrable systems lies at the boundary of mathematics and physics.
Integrable systems are universal limiting models of science that are widely applicable. The field grew from observations of astonishingly well-ordered and predictable behaviour in certain models of nonlinear lattices used to describe the thermal properties of metals and led to the theory of solitons and completely integrable systems, one of the most profound advances of twentieth century mathematics. Reductions led to the Painlevé equations, which are canonical representations of integrable models in one dimension.
Local blow up
Blow up space of initial conditions
The max-av composition of fuzzy relations R and S The max-av composition of fuzzy relations R and S
The max-product composition of fuzzy relations R and S The max-product composition of fuzzy relations R and S
The max-min composition of fuzzy relations R and S The max-min composition of fuzzy relations R and S
Fuzzy relation S Fuzzy relation S
Fuzzy relation R Fuzzy relation R
A tritronquée solution of the fourth Painlevé equation A tritronquée solution of the fourth Painlevé equation
An approximation of a tronquée solution of the fourth Painlevé equation An approximation of a tronquée solution of the fourth Painlevé equation
5-cube Orthogonal projection of 5-dimensional hypercube in 2D
Circle pattern Circle pattern corresponding to the discrete analogue
of holomorphic functions z^(4/5).
An algebraic curve with 5 ordinary singularities An algebraic curve with 5 ordinary singularities at (0,1), (0,-1), (1,0), (-1,0) and (0,0).
Initial value space of autonomous q-PIII Initial value space of autonomous q-PIII, wlog, we assume that b>a and d>c. D_i, i=1,2,3,4 are the divisors.
Second invariant curve for autonomous q-PIII in complex projective space These images represent the invariant curve for autonomous q-PIII in complex projective space. They show all 8 base points and potential duplicates.
Invariant curve for autonomous q-PIII in complex projective space These images represent the invariant curve for autonomous q-PIII in complex projective space. They show all 8 base points and potential duplicates.
Algebraic curve with 5 ordinary singularities f(x,y)=(x^4 + y^4 - x^2 - y^2)^2-9 x^2 y^2, an algebraic curve with 5 ordinary
singularities at (0,1), (0,-1), (1,0), (-1,0) and (0,0).
Configuration of the roots of a generalized Okamoto polynomial Configuration of the roots in the complex plane of one of the generalised Okamoto polynomials. These polynomials are associated with rational solutions of the fourth Painlevé equation. Why these roots are so beautifully organised remains a mystery.
Exponentially small waves present in the Frenkel Kontorova Model Exponentially small waves present in the far-field solution of the Frenkel-Kontorova model. The magnitude vanishes on the discrete points for which the solution is defined on
Time evolution of a 2-compacton initial condition While collisions of many kinds of solitary waves have been studied, the case of compactons is still an open question.
Tritronquée-type solutions to a modified Painlevé equation Real and imaginary tritronquée-type solutions to a modified Painlevé equation. The tritronquée-type solution is only valid within the indicated region. In the omitted region, elliptic functions are required to describe the solution behaviour.
Water waves past a submerged source Free-surface profile for potential flow of infinite depth flowing past a submerged source, containing steady waves generated in the downstream flow profile.
Staircase reduction Staircase reduction of the 7-point stencil of the discrete Euler-Lagrange equations of an ABS equation.
Ultra-Discrete KdV equation on a two dimensional domain Propagating from the singularity marked "1" eventually results in a region of singularities trapped by differential points.
Configuration of the bilinear discrete KP equation This figure shows 3 copies of the bilinear discrete Kadomtsev-Petviashvili system. This is a 3-dimensional lattice equation, which can be considered as relating 6 vertices of a cube.
Double Reflection Theorem
Interval Exchange Transformation
Lightlike Billiard Trajectories
Tropic curves and their light like tangents
Tropic curves on Confocal Quadrics in the Minkowski Space
The Integrable Systems Group currently consists of one Laureate Fellow, Nalini Joshi; a Research Associate, Milena Radnovic, two postdoctoral researchers, Pieter Roffelsen and Yang Shi; and six postgraduate students, Elynor Liu, Huda Alrashdi, Matthew Nolan, Michael Touitou, Shonal Singh, and Steven Luu.
Previous members of our group have gone on to work in research all over the world.
2017 Integrable Systems Workshop
We are hosting our fifth annual Workshop on Integrable Systems on 7 – 8 December 2017 at the School of Mathematics and Statistics, the University of Sydney.
Register by emailing the organisers at: email@example.com. Registrations close on 1 November 2017. You can find more information on the 2017 Integrable Systems Workshop page.
You can read information about our previous workshops:
- 2016 Integrable Systems Workshop
- 2015 Integrable Systems Workshop
- 2014 Integrable Systems Workshop
- 2013 Integrable Systems Workshop
In 2013 we commenced a series of workshops on integrable systems. These foster an exchange of ideas and encourage collaboration between mathematicians and research groups throughout Australia, and internationally.2017 Integrable Systems Workshop
Prof Allan Fordy, the University of Leeds, UK, visited 2013
Associate Prof Hayato Chiba, Kyushu University, Japan, visited 2017
Prof Peter Clarkson, University of Kent, visited 2016
A/Prof Anton Dzhamay, the University of Northern Colorado, USA, visited 2014
Dr Claire Gilson, the University of Glasgow, UK, visited 2015
Prof Claude Viallet, the U Pierre et Marie Curie, France, visited 2014 and 2015
Prof Da-jun Zhang, Shanghai University, visited 2014, 2016 and 2017
Dr Davide Masoero, Universidade de Lisboa, Portugal, visited 2015
Prof Harry Braden, the University of Edinburgh, visited 2016
Prof Frank Nijhoff, the University of Leeds, UK, visited 2015
Prof Mourad Ismail, the Université Grenoble Alpes, France, visited 2015
Prof Jarmo Hietarinta, the University of Turku, Finland, visited 2015
Prof Kenji Kajiwara, Kyushu University, Japan, visited 2013, 2016 and 2017
Dr Raphael Boll, the Technische Universität Berlin, Germany, visited 2015
A/Prof Takao Suzuki, Kindai University, visited 2016
Prof Teruhisa Tsuda, the University of Tokyo, Japan, visited 2014
Prof Walter Van Assche, the University of Leuven, Belgium, visited 2016
A/Prof Viktoria Heu, the Université de Strasbourg, France, visited 2014 and 2015
Prof Yasuhito Yamada, Kobe University, visited November 2016
A/Prof Yoshitsugu Takei, Kyoto University, visited 2013, 2015 and 2016