Name | Dim | Equation | Applications |
---|
Rayleigh | 1+1 | | |
Ricci flow | Any | | Poincaré conjecture |
Richards equation | 1+3 | | Variably saturated flow in porous media |
Rosenau–Hyman | 1+1 | | compacton solutions |
Sawada–Kotera | 1+1 | | |
Sack–Schamel equation | 1+1 | | plasmas |
Schamel equation | 1+1 | | plasmas, solitons, optics |
Schlesinger | Any | | isomonodromic deformations |
Seiberg–Witten | 1+3 | | Seiberg–Witten invariants, QFT |
Shallow water | 1+2 | | shallow water waves |
Sine–Gordon | 1+1 | | Solitons, QFT |
Sinh–Gordon | 1+1 | | Solitons, QFT |
Sinh–Poisson | 1+n | | Fluid Mechanics |
Swift–Hohenberg | any | | pattern forming |
Thomas | 2 | | |
Thirring | 1+1 | , | Dirac field, QFT |
Toda lattice | any | | |
Veselov–Novikov | 1+2 | , , | shallow water waves |
Vorticity equation | | | Fluid Mechanics |
Wadati–Konno–Ichikawa–Schimizu | 1+1 | | |
WDVV equations | Any | | Topological field theory, QFT |
WZW model | 1+1 |
| QFT |
Whitham equation | 1+1 | | water waves |
Williams spray equation | | | Combustion |
Yamabe | n | | Differential geometry |
Yang–Mills (source-free) | Any | | Gauge theory, QFT |
Yang–Mills (self-dual/anti-self-dual) | 4 | | Instantons, Donaldson theory, QFT |
Yukawa | 1+n | | Meson-nucleon interactions, QFT |
Zakharov system | 1+3 | | Langmuir waves |
Zakharov–Schulman | 1+3 | | Acoustic waves |
Zeldovich–Frank-Kamenetskii equation | 1+3 | | Combustion |
Zoomeron | 1+1 | | Solitons |
φ4 equation | 1+1 | | QFT |
σ-model | 1+1 | | Harmonic maps, integrable systems, QFT |