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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
See also
- List of quantum-mechanical systems with analytical solutions
- List of some well-known classical integrable systems
References
- 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.
- F. Calogero (2008) Calogero-Moser system. Scholarpedia, 3(8):7216.
- 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.
- 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.