Template:Integrable systems

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Geometric integrability

In classical mechanics

Examples	Harmonic oscillator Central force systems Kepler system Two body problem Integrable tops Euler Kovalevskaya Lagrange Garnier integrable system Hitchin system
Theory	Liouville-Arnold theorem Action-angle variables Superintegrable Hamiltonian system

In quantum mechanics

Integrable PDEs/Classical integrable field theories

Examples	KdV equation KdV hierarchy Sine-Gordon equation Nonlinear Schrodinger equation Gross-Neveu model Thirring model Kadomtsev-Petviashvili equation
Theory	Backlund transformation Lax pairs Infinitely many integrals of motion Soliton solutions Topological soliton Inverse scattering transform
ASDYM as a master theory	Anti-self-dual Yang-Mills equations Twistor correspondence Ward conjecture

Integrable Quantum Field theories

Master theories	Four-dimensional Chern-Simons theory (Lagrangian) Affine Gaudin models (Hamiltonian) Six-dimensional holomorphic Chern-Simons theory

Exactly solvable statistical lattice models

Exactly solvable quantum spin chains

Examples	Quantum Heisenberg model Gaudin model
Theory	Algebraic Bethe ansatz Quantum inverse scattering method Yang-Baxter equation

Contributors

Classical mechanics and geometry	Vladimir Arnold Leonhard Euler Ferdinand Georg Frobenius Nigel Hitchin Sofia Kovalevskaya Joseph-Louis Lagrange Joseph Liouville Simeon Denis Poisson
PDEs	Clifford S. Gardner John M. Greene Martin David Kruskal Peter Lax Robert Miura
IQFTs	Alexander Zamolodchikov Alexei Zamolodchikov
Classical and quantum statistical lattices	Rodney Baxter Ludvig Faddeev Elliott H. Lieb Yang Chen-Ning