List of integrable models
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{{Incomplete list|date=August 2008}}
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
Integrable models in 3+1 dimensions
- Self-dual Yang–Mills equations
- Systems with contact Lax pairs{{cite journal | last=Sergyeyev | first=A. | title=New integrable (3 + 1)-dimensional systems and contact geometry | journal=Letters in Mathematical Physics | publisher=Springer Science and Business Media LLC | volume=108 | issue=2 | date=2017-10-20 | issn=0377-9017 | doi=10.1007/s11005-017-1013-4 | pages=359–376|arxiv=1401.2122| bibcode=2018LMaPh.108..359S | s2cid=119159629 }}
In quantum mechanics
- harmonic oscillator
- hydrogen atom
- Hooke's atom (Hookium)
- Ruijsenaars–Schneider models
- Calogero–Moser modelsF. Calogero (2008) [http://www.scholarpedia.org/article/Calogero-Moser_system Calogero-Moser system]. Scholarpedia, 3(8):7216.
- Inverse square root potential
- Lambert-W step-potential{{cite journal | last=Ishkhanyan | first=A.M. | title=The Lambert- W step-potential – an exactly solvable confluent hypergeometric potential | journal=Physics Letters A | volume=380 | issue=5–6 | year=2016 | issn=0375-9601 | doi=10.1016/j.physleta.2015.12.004 | pages=640–644|arxiv=1509.00846| bibcode=2016PhLA..380..640I | s2cid=118513987 }}
- Multistate Landau–Zener Models{{cite journal | last1=Sinitsyn | first1=Nikolai A | last2=Chernyak | first2=Vladimir Y | title=The quest for solvable multistate Landau-Zener models | journal=Journal of Physics A: Mathematical and Theoretical | publisher=IOP Publishing | volume=50 | issue=25 | date=2017-05-24 | issn=1751-8113 | doi=10.1088/1751-8121/aa6800 | page=255203|arxiv=1701.01870| bibcode=2017JPhA...50y5203S | s2cid=119626598 }}