List of named differential equations
From Wikipedia, the free encyclopedia
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area.
Mathematics
- Ablowitz-Kaup-Newell-Segur (AKNS) system
- Clairaut's equation
- Hypergeometric differential equation
- Jimbo–Miwa–Ueno isomonodromy equations
- Painlevé equations
- Picard–Fuchs equation to describe the periods of elliptic curves
- Schlesinger's equations
- Sine-Gordon equation
- Sturm–Liouville theory of orthogonal polynomials and separable partial differential equations
- Universal differential equation
Algebraic geometry
- Calabi flow in the study of Calabi-Yau manifolds
Complex analysis
Differential geometry
- Equations for a minimal surface
- Liouville's equation
- Ricci flow, used to prove the Poincaré conjecture
- Tzitzeica equation
Dynamical systems and Chaos theory
Mathematical physics
- General Legendre equation
- Heat equation
- Ishimori equation, an integrable nonlinear spin field equation in 2+1 dimensions
- Laplace's equation in potential theory
- Poisson's equation in potential theory
Ordinary Differential Equations (ODEs)
Riemannian geometry
Physics
Astrophysics
Classical mechanics
Electromagnetism
- Bloch equations
- Continuity equation for conservation laws
- Maxwell's equations
- Poynting's theorem
Fluid dynamics and hydrology
- Acoustic theory
- Benjamin–Bona–Mahony equation
- Biharmonic equation
- Blasius boundary layer
- Boussinesq approximation (buoyancy)
- Boussinesq approximation (water waves)
- Buckley–Leverett equation
- Camassa–Holm equation
- Chaplygin's equation
- Continuity equation for conservation laws
- Convection–diffusion equation
- Davey–Stewartson equation
- Euler–Tricomi equation
- Falkner–Skan boundary layer
- Gardner equation in hydrodynamics
- General equation of heat transfer
- Geophysical fluid dynamics
- Groundwater flow equation
- Hicks equation
- Kadomtsev–Petviashvili equation in nonlinear wave motion
- KdV equation
- Magnetohydrodynamics
- Navier–Stokes equations
- Nonlinear Schrödinger equation in water waves
- Omega equation
- Orr–Sommerfeld equation
- Porous medium equation
- Potential flow
- Rayleigh–Bénard convection
- Rayleigh–Plesset equation
- Reynolds-averaged Navier–Stokes (RANS) equations
- Reynolds equation
- Reynolds transport theorem
- Riemann problem
- Taylor–von Neumann–Sedov blast wave
- Turbulence modeling
- Vorticity equation
- Whitham equation
- Zebiak-Cane model[1] for El Niño–Southern Oscillation
- Zeldovich–Taylor flow
General relativity
Materials science
Nuclear physics
Plasma physics
Quantum mechanics and quantum field theory
- Dirac equation, the relativistic wave equation for electrons and positrons
- Gardner equation
- Klein–Gordon equation
- Knizhnik–Zamolodchikov equations in quantum field theory
- Nonlinear Schrödinger equation in quantum mechanics
- Schrödinger equation[2]
- Schwinger–Dyson equation
- Yang-Mills equations in gauge theory
Thermodynamics and statistical mechanics
- Boltzmann equation
- Continuity equation for conservation laws
- Diffusion equation
- Kardar-Parisi-Zhang equation
- Kuramoto–Sivashinsky equation
- Liñán's equation as a model of diffusion flame
- Maxwell relations
- Zeldovich–Frank-Kamenetskii equation to model flame propagation
Waves (mechanical or electromagnetic)
- D'Alembert's wave equation
- Eikonal equation in wave propagation
- Euler–Poisson–Darboux equation in wave theory
- Helmholtz equation
Engineering
Electrical and Electronic Engineering
- Chua's circuit
- Liénard equation to model oscillating circuits
- Nonlinear Schrödinger equation in fiber optics
- Telegrapher's equations
- Van der Pol oscillator
Game theory
Mechanical engineering
Nuclear engineering
Optimal control
Orbital mechanics
Signal processing
Transportation engineering
Chemistry
Biology and medicine
- Allee effect in population ecology
- Bidomain model in cardiology
- Chemotaxis[7] in wound healing
- Compartmental models in epidemiology
- SIR model
- SIS model
- Hagen–Poiseuille equation in blood flow
- Hodgkin–Huxley model in neural action potentials
- Kardar–Parisi–Zhang equation for bacteria surface growth models
- Kermack-McKendrick theory in infectious disease epidemiology
- Kuramoto model in biological and chemical oscillations
- Mackey-Glass equations
- McKendrick–von Foerster equation in age structure modeling
- Nernst–Planck equation in ion flux across biological membranes
- Price equation in evolutionary biology
- Reaction-diffusion equation in theoretical biology
- Fisher–KPP equation in nonlinear traveling waves
- FitzHugh–Nagumo model in neural activation
- Swift-Hohenberg equation in pattern formation
- Replicator dynamics in theoretical biology
- Verhulst equation in biological population growth
- von Bertalanffy model in biological individual growth
- Wilson–Cowan model in computational neuroscience
Population dynamics
- Arditi–Ginzburg equations to describe predator–prey dynamics
- Kolmogorov–Petrovsky–Piskunov equation (also known as Fisher's equation) to model population growth
- Logistic differential equation, for population growth
- Generalized logistic differential equation for growth modeling
- Lotka–Volterra equations to describe the dynamics of biological systems in which two species interact
Economics and finance
- Bass diffusion model
- Black–Scholes equation
- Economic growth
- Feynman–Kac formula
- Fokker–Planck equation
- Dupire equation (local volatility)
- Hamilton–Jacobi–Bellman equation
- Malthusian growth model
- Mean field game theory[10]
- Optimal rotation age
- Sovereign debt accumulation
- Stochastic differential equation
- Vidale–Wolfe advertising model
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Linguistics
Military strategy
- Lanchester's laws in combat modeling