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
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
References
- ↑ A. Sergyeyev (2018). New integrable (3 + 1)-dimensional systems and contact geometry, Lett. Math. Phys. 108, no. 2, 359–376, arXiv:1401.2122 doi:10.1007/s11005-017-1013-4
- ↑ F. Calogero (2008) Calogero-Moser system. Scholarpedia, 3(8):7216.
- ↑ A. Ishkhanyan (2016), The Lambert-W step-potential - an exactly solvable confluent hypergeometric potential, arXiv:1509.00846, Phys. Lett. A 380, 640-644
- ↑ N. A. Sinitsyn; V. Y. Chernyak (2017). "The Quest for Solvable Multistate Landau–Zener Models". arXiv:1701.01870 [quant-ph].
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