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[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

References

1. Sergyeyev, A. (2017-10-20). "New integrable (3 + 1)-dimensional systems and contact geometry". Letters in Mathematical Physics. 108 (2). Springer Science and Business Media LLC: 359–376. arXiv:1401.2122. Bibcode:2018LMaPh.108..359S. doi:10.1007/s11005-017-1013-4. ISSN 0377-9017. S2CID 119159629.
2. F. Calogero (2008) Calogero-Moser system. Scholarpedia, 3(8):7216.
3. Ishkhanyan, A.M. (2016). "The Lambert- W step-potential – an exactly solvable confluent hypergeometric potential". Physics Letters A. 380 (5–6): 640–644. arXiv:1509.00846. Bibcode:2016PhLA..380..640I. doi:10.1016/j.physleta.2015.12.004. ISSN 0375-9601. S2CID 118513987.
4. Sinitsyn, Nikolai A; Chernyak, Vladimir Y (2017-05-24). "The quest for solvable multistate Landau-Zener models". Journal of Physics A: Mathematical and Theoretical. 50 (25). IOP Publishing: 255203. arXiv:1701.01870. Bibcode:2017JPhA...50y5203S. doi:10.1088/1751-8121/aa6800. ISSN 1751-8113. S2CID 119626598.