Discrete Integrable Systems
Treat integrable maps, lattice equations, recurrences and discrete geometric structures as subjects in their own right.
This volume will develop the subjects in the chapter map below. Use the outline to locate the methods and examples you want to study; the individual readings are still being developed.
Learning sequences: Open Toda · The XXX spin chain · KdV solitons · Finite-ring TASEP
Readings and planned coverage
CHAPTER 01
Integrable maps & recurrences
Planned coverage
- QRT maps
CHAPTER 02
Lattice equations & multidimensional consistency
Planned coverage
- Consistency around a cube
CHAPTER 03
Discrete Lax pairs & dressing transformations
Planned coverage
- Lax representations of lattice equations
CHAPTER 04
Discrete Painlevé systems
Planned coverage
- Discrete Painlevé equations and spaces of initial conditions
CHAPTER 05
Cluster algebras & bilinear recurrences
Planned coverage
- Cluster mutations and integrable recurrences
CHAPTER 06
Discrete variational & geometric structures
Planned coverage
- Lagrangian multiforms
CHAPTER 07
Ultradiscrete systems & cellular automata
Planned coverage
- The box–ball system