Clebsch and Steklov systems in fluids Calogero–Moser–Sutherland model Integrable lattice models Toda lattice Ablowitz–Ladik lattice Volterra lattice Integrable systems in 1 + 1 dimensions Korteweg–de Vries equation Sine–Gordon equation Nonlinear Schrödinger equation AKNS system Boussinesq equation (water waves) Camassa–Holm equation Nonlinear sigma models Classical Heisenberg ferromagnet model (spin chain) Classical Gaudin spin system (Garnier system) Kaup–Kupershmidt equation Krichever–Novikov equation Landau–Lifshitz equation (continuous spin field) Benjamin–Ono equation Degasperis–Procesi equation Dym equation Massive Thirring model Three-wave equation Integrable PDEs in 2 + 1 dimensions Kadomtsev–Petviashvili equation Davey–Stewartson equation Ishimori equation Novikov–Veselov equation The Belinski–Zakharov transform generates a Lax pair for the Einstein field equations; general solutions are termed gravitational solitons, of which the Schwarzschild metric, the Kerr metric and some gravitational wave solutions are examples. Exactly solvable statistical lattice models Ising model in 1- and 2-dimensions Ice-type model of Lieb 8-vertex model See also Hitchin system Related areas Mathematical physics Soliton Painleve transcendents Statistical mechanics Integrable algorithm Some key contributors (since 1965) References Further reading External links "SIDE - Symmetries and Integrability of Difference Equations", a conference devoted to the study of integrable difference equations and related topics. Notes Dynamical systems Hamiltonian mechanics Partial differential equations