See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations.
A–F {|class="wikitable" style="text-align: left" |-style="background: #eee" !Name !Dim !Equation !Applications |- |Bateman-Burgers equation |1+1 | |Fluid mechanics |- |Benjamin–Bona–Mahony |1+1 | |Fluid mechanics |- |Benjamin–Ono |1+1 | | internal waves in deep water |- |Boomeron |1+1 | |Solitons |- |Boltzmann equation |1+6 |
|Statistical mechanics |- |Born–Infeld |1+1 | | Electrodynamics |- |Boussinesq | 1+1 | |Fluid mechanics |- |Boussinesq type equation | 1+1 | |Fluid mechanics |- |Buckmaster |1+1 | |Thin viscous fluid sheet flow |- |Cahn–Hilliard equation |Any | |Phase separation |- |Calabi flow |Any | |Calabi–Yau manifolds |- | Camassa–Holm |1+1 | |Peakons |- |Carleman |1+1
||Cauchy momentum |any | |Momentum transport |- | Chafee–Infante equation
|Clairaut equation |any | |Differential geometry |- |Clarke's equation |1+1 | |Combustion |- |Complex Monge–Ampère |Any | lower order terms |Calabi conjecture |- |Constant astigmatism |1+1 | |Differential geometry |- |Davey–Stewartson |1+2 | |Finite depth waves |- |Degasperis–Procesi |1+1 | |Peakons |- |Dispersive long wave |1+1 |,
|Drinfeld–Sokolov–Wilson |1+1
|Dym equation |1+1 | |Solitons |- |Eckhaus equation |1+1 | |Integrable systems |- |Eikonal equation |any | |optics |- |Einstein field equations | Any | |General relativity |- |Erdogan–Chatwin equation |1+1 | |Fluid dynamics |- |Ernst equation |2
| Estevez–Mansfield–Clarkson equation
|Euler equations |1+3 | |non-viscous fluids |- |Fisher's equation |1+1 | |Gene propagation |- |FitzHugh–Nagumo model |1+1 | |Biological neuron model |- |Föppl–von Kármán equations
|Solid Mechanics |- | Fujita–Storm equation
G–K {|class="wikitable" style="text-align: left" |-style="background: #eee" !Name !Dim !Equation !Applications |- |G equation |1+3 | | turbulent combustion |- |Generic scalar transport |1+3 | |transport |- |Ginzburg–Landau |1+3 | |Superconductivity |- |Gross–Pitaevskii
| Bose–Einstein condensate |- |Gyrokinetics equation
| Microturbulence in plasma |- ||Guzmán
| Hamilton–Jacobi–Bellman equation for risk aversion |- |Hartree equation |Any
|Hasegawa–Mima |1+3 | |Turbulence in plasma |- |Heisenberg ferromagnet |1+1 | |Magnetism |- |Hicks |1+1 | |Fluid dynamics |- |Hunter–Saxton |1+1 | |Liquid crystals |- |Ishimori equation |1+2 | |Integrable systems |- |Kadomtsev –Petviashvili |1+2 | |Shallow water waves |- |Kardar–Parisi–Zhang equation |1+3 | |Stochastics |- |von Karman |2
|Kaup |1+1
|Kaup–Kupershmidt |1+1 | |Integrable systems |- |Klein–Gordon–Maxwell |any
|Klein–Gordon (nonlinear) |any | | Relativistic quantum mechanics |- |Khokhlov–Zabolotskaya |1+2
|Kompaneyets |1+1 | |Physical kinetics |- |Korteweg–de Vries (KdV) |1+1 | |Shallow waves, Integrable systems
|KdV (super) |1+1
|colspan="4" |There are many different variations listed in the article on KdV equations. |- |Kuramoto–Sivashinsky equation
|Combustion
L–Q {|class="wikitable" style="text-align: left" |-style="background: #eee" !Name !Dim !Equation !Applications |- |Landau–Lifshitz model |1+n | |Magnetic field in solids |- |Lin–Tsien equation |1+2
|Liouville equation |any
|Liouville–Bratu–Gelfand equation |any | |combustion, astrophysics |- |Logarithmic Schrödinger equation |any | |Superfluids, Quantum gravity |- |Minimal surface |3 | |minimal surfaces |- |Monge–Ampère |any | lower order terms
|Navier–Stokes(and its derivation) |1+3 | + mass conservation: + an equation of state to relate p and ρ, e.g. for an incompressible flow: |Fluid flow, gas flow |- |Nonlinear Schrödinger (cubic) |1+1 | |optics, water waves |- |Nonlinear Schrödinger (derivative) |1+1 | |optics, water waves |- |Omega equation |1+3 | |atmospheric physics |- |Plateau |2 | |minimal surfaces |- |Pohlmeyer–Lund–Regge |2
|Porous medium |1+n | |diffusion |- |Prandtl |1+2 |, |boundary layer
R–Z, α–ω {|class="wikitable" style="text-align: left" |-style="background: #eee" !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
References