Learn Integrable Systems

Build understanding through worked examples, practice, and connections. Classical and quantum integrability are parallel starting points; specialist routes let you enter from the mathematics or physics you already know.

For a first encounter, read What makes a system integrable?. A nonlinear oscillator shows why integrability needs a precise claim; short examples then connect that idea to the routes below.

Choose the open Toda sequence to study particle motion, Lax pairs and classical integrability; the XXX spin-chain sequence to work from quantum spin flips to Bethe equations; the KdV sequence to connect a solitary wave with inverse scattering; or finite-ring TASEP to derive a stochastic current and test a Bethe decay mode. All four offer targeted preparation, solved exercises and reproducible computations.

Use Start & Prepare to compare their entry requirements and try a diagnostic calculation. Use Practice & Projects to find the available experiments. These are independent entrances; the broader outlines below describe further courses.