List of Some Well-known Classical Integrable Systems
1. Classical mechanical systems (finite-dimensional phase space):
- Harmonic oscillators in n dimensions
- Central force motion
- Two center Newtonian gravitational motion
- Geodesic motion on ellipsoids
- Neumann oscillator
- Lagrange, Euler and Kovalevskaya tops
- Integrable Clebsch and Steklov systems in fluids
- Calogero–Moser–Sutherland models
- Swinging Atwood's Machine with certain choices of parameters
2. Integrable lattice models
- Toda lattice
- Ablowitz–Ladik lattice
- Volterra lattice
3. Integrable systems of PDEs in 1 + 1 dimension
- Korteweg–de Vries equation
- Sine–Gordon equation
- Nonlinear Schrödinger equation
- Boussinesq equation (water waves)
- Nonlinear sigma models
- Classical Heisenberg ferromagnet model (spin chain)
- Classical Gaudin spin system (Garnier system)
- Landau–Lifshitz equation (continuous spin field)
- Benjamin–Ono equation
- Dym equation
- Three wave equation
4. Integrable PDEs in 2 + 1 dimensions
- Kadomtsev–Petviashvili equation
- Davey–Stewartson equation
- Ishimori equation
5. Other integrable systems of PDEs in higher dimensions
- Self-dual Yang–Mills equations
Read more about this topic: Integrable System
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