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Willox Lab
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The lab studies soliton equations and Painlevé equations by discretizing them.
AboutAbout the lab
Bringing solvable nonlinear equations into the discrete world
The Willox Lab studies "integrable nonlinear equations" that arise in mathematical physics.
In particular, it focuses on soliton equations and Painlevé equations, as well as their discretized counterparts.
Using Hirota's bilinear method and Sato theory as its main tools, the lab aims to extend ideas known from continuous systems, such as symmetries and conserved quantities, to difference equations and cellular automata.
The lab also investigates the discretization of continuous models that describe natural phenomena, using both computer simulation and analytical methods.
Key terms
- Soliton equation
- A nonlinear equation whose solutions include solitons, isolated waves that travel without changing shape
- Difference equation
- An equation that treats time and space as discrete values and describes change through relationships between neighboring values
- Cellular automaton
- A computational model in which the states of the cells on a grid all change simultaneously according to fixed rules
ResearchResearch themes
The lab studies integrable nonlinear equations that arise in mathematical physics, particularly soliton equations and Painlevé equations and their discretizations. It also investigates the discretization of continuous models and the properties of cellular automata obtained as their ultradiscrete limits.
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MembersFaculty
- ProfessorRalph WilloxPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Two soliton overtake collision - color plot” N0fk / CC BY-SA 4.0 (cropped)
- Integrable Systems and Discrete Dynamical Systems: “Time Evolution of the Box-Ball System” 黒猫の
デルタ / CC0 (cropped) - Related lab (Hayashi Lab): “Lorenz attractor and its transients” Yapparina / CC0 (cropped)
- Related lab (Kato Lab): “Orange Genus 2 Surface” Gelada / CC BY-SA 3.0 (cropped)
- Related lab (Matsui Lab): “Illustration of Yang Baxter Equation” AHusain314 / Public domain (cropped)
- Related lab (Shiraishi Lab): “Weierstrass p function” Claudio Rocchini / CC BY-SA 4.0 (cropped)
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