List of integrable models explained

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^[1]

In quantum mechanics

• harmonic oscillator
• hydrogen atom
• Hooke's atom (Hookium)
• Ruijsenaars–Schneider models
• Calogero–Moser models^[2]
• Inverse square root potential
• Lambert-W step-potential^[3]
• Multistate Landau–Zener Models^[4]

See also

• List of quantum-mechanical systems with analytical solutions
• List of some well-known classical integrable systems

Notes and References

1. Sergyeyev . A. . New integrable (3 + 1)-dimensional systems and contact geometry . Letters in Mathematical Physics . Springer Science and Business Media LLC . 108 . 2 . 2017-10-20 . 0377-9017 . 10.1007/s11005-017-1013-4 . 359–376. 1401.2122. 2018LMaPh.108..359S . 119159629 .
2. [Francesco Calogero|F. Calogero]
3. Ishkhanyan . A.M. . The Lambert- W step-potential – an exactly solvable confluent hypergeometric potential . Physics Letters A . 380 . 5–6 . 2016 . 0375-9601 . 10.1016/j.physleta.2015.12.004 . 640–644. 1509.00846. 2016PhLA..380..640I . 118513987 .
4. Sinitsyn . Nikolai A . Chernyak . Vladimir Y . The quest for solvable multistate Landau-Zener models . Journal of Physics A: Mathematical and Theoretical . IOP Publishing . 50 . 25 . 2017-05-24 . 1751-8113 . 10.1088/1751-8121/aa6800 . 255203. 1701.01870. 2017JPhA...50y5203S . 119626598 .