Library of Integrable Systems

Explore integrable systems in depth through sixteen subject volumes. Each volume provides a chapter map; the collection connects classical mechanics, nonlinear waves, quantum systems, geometry, probability, and applications.

The volumes are entrances, not a compulsory sequence. Current derivations establish finite open Toda integrability, construct XXX eigenstates and a complete four-site sector, prove the commuting-transfer-matrix mechanism, reconstruct one- and two-soliton KdV fields, and derive a two-particle Bethe mode for periodic TASEP. Find these readings directly below, before exploring the wider sixteen-volume map.

Choose a question or system first, then use the relevant mathematical tools. Learn provides guided calculations and practice; Models fixes the equations and regimes; Reference supplies convention translations and checked source editions. Unlinked chapter titles describe material still to be written.