List of Nonlinear Partial Differential Equations - List of Equations - A–F

A–F

Name Dim Equation Applications
Benjamin–Bona–Mahony 1+1 Fluid mechanics
Benjamin-Ono 1+1 internal waves in deep water
Boomeron 1+1

displaystyle mathbf{v}_{xt}=u_{xx}mathbf{b}+mathbf{a}timesmathbf{v}_x-
2mathbf{v}times(mathbf{v}timesmathbf{b})

Solitons
Born-Infeld 1+1
Boussinesq 1+1 Fluid mechanics
Buckmaster 1+1 Thin viscous fluid sheet flow
Burgers 1+1 Fluid mechanics
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
Caudrey–Dodd–Gibbon–Sawada–Kotera 1+1 Same as (rescaled) Sawada–Kotera
Chiral field 1+1
Clairaut equation any Differential geometry
Complex Monge–Ampère Any lower order terms Calabi conjecture
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
Ernst equation 2
Euler equations 1+3 
begin{align}
&{partialrhooverpartial t}+
nablacdot(rhobold u)=0\
&{partialrho{bold u}overpartial t}+
nablacdot(bold uotimes(rho bold bold u))+nabla p=0\
&{partial Eoverpartial t}+
nablacdot(bold u(E+p))=0,
end{align}
non-viscous fluids
Fisher's equation 1+1 Gene propagation
Fitzhugh-Nagumo 1+1

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