List of integrable models

This is a list of integrable models as well as classes of integrable models in physics.

Integrable models in 1+1 dimensions
In classical and quantum field theory:


 * free boson
 * free fermion
 * sine-Gordon model
 * Thirring model
 * sinh-Gordon model
 * Liouville field theory
 * Bullough–Dodd model
 * Dym equation
 * Calogero–Degasperis–Fokas equation
 * Camassa–Holm equation
 * Drinfeld–Sokolov–Wilson equation
 * Benjamin–Ono equation
 * SS model
 * sausage model
 * Toda field theories
 * O(N)-symmetric non-linear sigma models
 * Ernst equation
 * massless Schwinger model
 * supersymmetric sine-Gordon model
 * supersymmetric sinh-Gordon model
 * conformal minimal models
 * critical Ising model
 * tricritical Ising model
 * 3-state Potts model
 * various perturbations of conformal minimal models
 * superconformal minimal models
 * Wess–Zumino–Witten model
 * Nonlinear Schroedinger equation
 * Korteweg–de Vries equation
 * modified Korteweg–de Vries equation
 * Gardner equation
 * Gibbons–Tsarev equation
 * Hunter–Saxton equation
 * Kaup–Kupershmidt equation
 * XXX spin chain
 * XXZ spin chain
 * XYZ spin chain
 * 6-vertex model
 * 8-vertex model
 * Kondo Model
 * Anderson impurity model
 * Chiral Gross–Neveu model

Integrable models in 2+1 dimensions

 * Ishimori equation
 * Kadomtsev–Petviashvili equation
 * Landau–Lifshitz–Gilbert equation
 * Novikov–Veselov equation

Integrable models in 3+1 dimensions

 * Self-dual Yang–Mills equations
 * Systems with contact Lax pairs

In quantum mechanics

 * harmonic oscillator
 * hydrogen atom
 * Hooke's atom (Hookium)
 * Ruijsenaars–Schneider models
 * Calogero–Moser models
 * Inverse square root potential
 * Lambert-W step-potential
 * Multistate Landau–Zener Models