Encyclopedia of Nonlinear Science

(List is not final and is subject to change prior to publication.)

History of Nonlinear Science
Common Examples of Nonlinear Phenomena
Analytical Methods
Computational Methods
Topological Methods
Chaos, Noise, and Turbulence
Coherent Structures
Dynamical Systems
General Phenomena
Maps
Mathematical Models
Stability
Astronomy and Astrophysics
Biology
Chemistry
Condensed Matter and Solid-State Physics
Earth Science
Engineering
Fluids
Neuroscience
Nonlinear Optics
Plasma Physics
Social Science
Solid Mechanics and Nonlinear Vibrations
Theoretical Physics

History of Nonlinear Science

Butterfly effect
Candle Integrability
Celestial mechanics
Davydov soliton
Determinism
Feedback
Fermi-Pasta-Ulam oscillator chain
Fibonacci series
Hodgkin-Huxley equations
Lorenz equations
Manley-Rowe relations
Markin-Chizmadzhev model
Martingales
Matter, nonlinear theory of
Poincaré theorems
Preface
Solar system
Soliton
a brief history
Tacoma Narrows Bridge collapse
Van der Pol equation
Zeldovich-Frank-Kamenetsky equation

Common Examples of Nonlinear Phenomena

Avalanches
Ball lightning
Brownian motion
Butterfly effect
Candle
Clear air turbulence
Dripping faucet
Dune formation
Explosions
Fairy rings of mushrooms
Filamentation
Flame front
Fluid dynamics
Forest fires
Glacial flow
Global warming
Hurricanes and tornadoes
Jupiter's Great Red Spot
Nonlinear toys
Order from chaos
Pendulum
Phase transitions
Plume dynamics
Solar system
Tacoma Narrows Bridge collapse
Traffic flow
Water waves

Analytical Methods

Bäcklund transformations
Bethe ansatz
Center-manifold reduction
Characteristics
Collective coordinates
Continuum approximations
Dimensional analysis
Dispersion relations
Dressing method
Elliptic functions
Energy analysis
Evans function
Fredholm theorem
Gel'fand-Levitan theory
Generalized functions
Hamiltonian systems
Hirota's method
Hodograph transform
Idempotent analysis
Inverse scattering method
Integrable transforms
Kirchhoff laws
Multiple scale analysis
Multisoliton perturbation theory
Nonequilibrium statistical mechanics
Normal forms theory
N-soliton formulas
Painlevé analysis
Periodic spectral theory
Perturbation theory
Phase dynamics
Poisson brackets
Power balance
Quantum inverse scattering method
Quasilinear analysis
Riccati equations
Rotating wave approximation
Separation of variables
Spectral analysis
Stability
State diagrams
Synergetics
Tensors
Theta functions
Time series analysis
Volterra series
Zero-dispersion limits

Computational Methods

Averaging methods
Cellular automata
Cellular nonlinear networks
Characteristics
Compartmental models
Contour dynamics
Embedding methods
Extremum principles
Fitness landscape
Forecasting
Framed space curves
Hartree approximation
Integrability
Inverse problems
Lattice gas methods
Linearization
Maps
Martingales
Monte-Carlo methods
Numerical methods
Recurrence
Theta functions
Time series analysis
Visiometrics
Volterra series
Wavelets

Topological Methods

Conley index
Cat map
Darboux transformation
Denjoy theory
Derrick-Hobart theorem
Differential geometry
Extremum principles
Functional analysis
Horseshoes and hyperbolicity
Huygens' principle
Inertial manifolds
Invariant manifolds and sets
Knot theory
Kolmogorov-Arnold-Moser theory
Lie algebras and Lie groups
Maps
Measures
Monodromy-preserving deformations
Multifractal analysis
Nontwist maps
One-dimensional maps
Periodic orbit theory
Phase space
Renormalization groups
Riemann-Hilbert problem
Singularity theory
Symbolic dynamics
Symmetry groups
Topology
Virial theorem
Winding numbers

Chaos, Noise, and Turbulence

Attractors
Aubry-Mather theory
Butterfly effect
Chaos vs. turbulence
Chaotic advection
Chaotic dynamics
Clear air turbulence
Dimensions
Entropy
Ergodic theory
Fluctuation-dissipation theorem
Fokker-Planck equation
Free probability theory
Frustration
Hele-Shaw experiment
Horseshoes and hyperbolicity
Lagrangian chaos
Levy flights
Lyapunov exponents
Martingales
Melnikov method
Order from chaos
Percolation theory
Phase space analysis
Quantum chaos
Random matrix theory
Random walks
Routes to chaos
Spatiotemporal chaos
Stochastic processes
Turbulence
Turbulence, ideal

Coherent Structures

Biomolecular solitons
Black holes
Breathers
Cell assemblies
Davydov soliton
Discrete breathers
Dislocations in crystals
DNA solitons
Domain walls
Dune formation
Emergence
Fairy rings of mushrooms
Flame front
Higgs boson
Holons
Hurricanes and tornadoes
Instantons
Jupiter's Great Red Spot
Local modes in molecular crystals
Local modes in molecules
Multidimensional solitons
Nerve impulses
Polariton
Polaron
Shock waves
Skyrmions
Solitons, types of
Spiral waves
Tachyons and superluminal motion
Turing patterns
Wave of translation

Dynamical Systems

Anosov/axiom A system
Arnold diffusion
Attractors
Aubry-Mather theory
Bifurcations
Billiards
Butterfly effect
Catastrophe theory
Cat map
Center-manifold reduction
Chaotic dynamics
Coupled map lattice
Deterministic walks in random environment
Development of singularities
Dynamical systems
Equilibrium
Ergodic theory
Fitness landscape
Framed space curves
Function spaces
Gradient system
Hamiltonian systems
Hénon map
Hopf bifurcation
Horseshoes and hyperbolicity
Inertial manifolds
Intermittency
Kicked rotor
Kolmogorov-Arnold-Moser theory
Lyapunov exponents
Maps
Measures
Melnikov method
One-dimensional maps
Pattern formation
Periodic orbit theory
Phase plane
Phase space
Phase space diffusion and correlations
Poincaré theorems
Reaction diffusion systems
Rössler systems
Rotating rigid bodies
Routes to chaos
Sinai-Ruelle-Bowen measure
Standard map
Stochastic processes
Symbolic dynamics
Synergetics
Universality
Visiometrics
Winding numbers

General Phenomena

Adiabatic invariants
Algorithmic complexity
Anderson localization
Arnold diffusion
Attractors
Berry's phase
Bifurcations
Binding energy
Boundary layers
Branching laws
Breathers
Brownian motion
Butterfly effect
Causality
Chaotic dynamics
Characteristics
Cluster coagulation
Coherence phenomena
Collisions
Critical phenomena
Detailed balance
Determinism
Diffusion
Domain walls
Doppler shift
Effective mass
Emergence
Entropy
Equilibria
Equipartition of energy
Excitability
Explosions
Feedback
Filamentation
Fractals
Free energy
Frequency doubling
Frustration
Gestalt phenomena
Group velocity
Harmonic generation
Helicity
Hopf bifurcation
Hysteresis
Incoherent solitons
Inhibition
Integrability
Intermittency
Jump phenomena
Kolmogorov cascade
Levy flights
Lifetime
Mixing
Modulated waves
Multiplicative processes
Nonlinearity, definition of
N-wave interactions
Order from chaos
Order parameters
Overtones
Pattern formation
Period doubling
Periodic bursting
Power balance
Quantum chaos
Quantum nonlinearity
Quasiperiodicity
Recurrence
Routes to chaos
Scroll waves
Shear flow
Solitons
Spiral waves
Structural complexity
Symmetry: equations vs. solutions
Synergetics
Tessellation
Thermal convection
Threshold phenomena
Turbulence
Universality
Wave packets, linear and nonlinear
Wave propagation in disordered media
Wave stability and instability

Maps

Aubry-Mather theory
Bäcklund transforms
Cat map
Coupled map lattice
Darboux transformation
Denjoy theory
Embedding methods
Fermi acceleration and Fermi map
Hénon map
Maps
Maps in the complex plane
Monodromy-preserving deformations
Nontwist maps
One-dimensional maps
Periodic orbit theory
Recurrence
Renormalization groups
Singularity theory
Standard map
Symplectic maps

Mathematical Models

Ablowitz-Kaup-Newell-Segur system
Attractor neural networks
Billiards
Boundary-value problems
Brusselator
Burgers equation
Cat map
Cellular automata
Compartmental models
Complex Ginzburg-Landau equation
Continuum approximations
Coupled map lattice
Coupled systems of partial differential equations
Delay-differential equations
Difference equations
Discrete nonlinear Schrödinger equations
Discrete self-trapping system
Duffing equation
Equations, nonlinear
Euler-Lagrange equations
Fitzhugh-Nagumo equation
Fokker-Planck equation
Frenkel-Kontorova model
Game of life
General circulation models of the atmosphere
Hénon-Heiles system
Integrable cellular automata
Integrable lattices
Ising model
Kadomtsev-Petviashvili equation
Knot theory
Korteweg-de Vries equation
Kuramoto-Sivashinsky equation
Landau-Lifshitz equation
Lattice gas methods
Lie algebras and Lie groups
Lorenz model
Markov partitions
Martingales
Maxwell-Bloch system
McCulloch-Pitts network
Navier-Stokes equation
Neural network models
Newton's laws of motion
Nonlinear Schrödinger equations
One-dimensional maps
Ordinary differential equations, nonlinear
Partial differential equations, nonlinear
Random walks
Riccati equations
Salerno equation
Sandpile model
Sine-Gordon equation
Spin systems
Stochastic processes
Symbolic dynamics
Synergetics
Toda lattice
Van der Pol equation
Zeldovich-Frank-Kamenetsky equation

Stability

Attractors
Bifurcations
Butterfly effect
Catastrophe theory
Controlling chaos
Development of singularities
Dispersion management
Dispersion relations
Emergence
Equilibrium
Excitability
Feedback
Growth patterns
Hopf bifurcation
Lyapunov exponents
Nonequilibrium statistical mechanics
Stability

Astronomy and Astrophysics

Alfven waves
Black holes
Celestial mechanics
Cosmological models
Einstein equations
Galactic dynamics
Gravitational waves
Hénon-Heiles system
Jupiter's Great Red Spot
N-body problem
Solar system

Biology

Artificial life
Bilayer lipid membranes
Biological evolution
Biomolecular solitons
Cardiac muscle models
Catalytic hypercycle
Compartmental models
Davydov soliton
DNA premelting
DNA solitons
Cardiac arrhythmias and electrocardiogram
Cardiac muscle models
Epidemiology
Excitability
Fairy rings of mushrooms
Fibonacci series
Fitness landscape
Frohlich theory
Game of life
Growth patterns
Holons
Morphogenesis, biological
Nephron dynamics
Protein dynamics
Protein structure
Scroll waves
Turing patterns
Synergetics

Chemistry

Belousov-Zhabotinsky reaction
Biomolecular solitons
Brusselator
Candle
Catalytic hypercycle
Chemical kinetics
Flame front
Franck-Condon factor
Hydrogen bond
Langmuir-Blodgett films
Molecular dynamics
Oregonator
Polymerization
Protein structure
Reaction-diffusion systems
Scheibe aggregates
Vortex dynamics in excitable media

Condensed Matter and Solid-State Physics

Anderson localization
Avalanche breakdown
Bjerrum defects
Bose-Einstein condensation
Charge density wave
Cherenkov radiation
Color centers
Commensurate-incommensurate transition
Discrete breathers
Dislocations in crystals
Domain walls
Drude model
Effective mass
Excitons
Ferroelectricity and ferromagnetism
Franck-Condon factor
Frenkel-Kontorova model
Frustration
Heat conduction
Hydrogen bond
Ising model
Langmuir-Blodgett films
Liquid crystals
Local modes in molecular crystals
Mechanics of solids
Nonlinear acoustics
Peierls barrier
Percolation theory
Regular and chaotic dynamics in atomic physics
Scheibe aggregates
Semiconductor oscillators
Spin systems
Superconductivity
Superfluidity

Earth Science

Alfvèn waves
Angle of repose
Atmospheric and ocean sciences
Avalanches
Ball lightning
Butterfly effect
Clear air turbulence
Dune formation
Fairy rings of mushrooms
Forest fires
General circulation models of the atmosphere
Geomorphology and tectonics
Glacial flow
Global warming
Hurricanes and tornadoes
Kelvin-Helmholtz instability
Sandpile model
Water waves

Engineering

Artificial intelligence
Cellular automata
Cellular nonlinear networks
Chua's circuit
Controlling chaos
Coupled oscillators
Diodes
Dispersion management
Dynamos, homogeneous
Electron beam devices
Explosions
Feedback
Flip-flop circuit
Frequency doubling
Information theory
Hysteresis
Josephson junction arrays
Josephson junctions
Langmuir-Blodgett films
Lasers
Long Josephson junction
Manley-Rowe relations
Neuristor
Nonlinear electronics
Nonlinear optics
Nonlinear signal processing
Optical fiber communications
Parametric amplification
Particle accelerators
Ratchets
Relaxation oscillators
Semiconductor laser
Semiconductor oscillators
Superconducting quantum interference device
Synchronization
Tacoma Narrows Bridge collapse

Fluids

Alfven waves
Atmospheric and ocean sciences
Bernoulli's equation
Clear-air turbulence
Contour dynamics
Electron beam devices
Evaporation wave
Fluid dynamics
Forecasting
General circulation models of the atmosphere
Glacial flow
Hurricanes and tornadoes
Hydrothermal waves
Jump phenomena
Jupiter's Great Red Spot
Kelvin-Helmholtz instability
Laboratory models of nonlinear waves
Lattice gas methods
Liquid crystals
Lorentz gas
Magnetohydrodynamics
Navier-Stokes equation
Nonlinear plasma waves
Plasma soliton experiments
Plume dynamics
Rayleigh-Taylor instability
Shear flow
Shock waves
Superfluidity
Surface waves
Taylor-Couette flow
Thermal convection
Thermo-diffusion effects
Traffic flow
Turbulence
Turbulence, ideal
Visiometrics
Vortex dominated flows
Water waves

Neuroscience

Artificial intelligence
Attractor neural network
Cell assemblies
Compartmental models
Depth perception and binocular rivalry
Electroencephalogram at large scales
Electroencephalogram at mesoscopic scales
Ephaptic coupling
Evans function
Gestalt phenomena
Hodgkin-Huxley equations
Integrate and fire neuron
Multiplex neuron
Myelinated nerves
Nerve impulses
Neural network models
Neurons
Pattern formation
Perceptron
Stochastic analyses of neural systems
Synergetics

Nonlinear Optics

Damped driven anharmonic oscillator
Cherenkov radiation
Color centers
Dispersion management
Distributed oscillators
Excitons
Filamentation
Geometrical optics, nonlinear
Harmonic generation
Hole burning
Kerr effect
Lasers
Liquid crystals
Maxwell-Bloch system
Nonlinear optics
Optical fiber communications
Photonic crystals
Polariton
Polaron
Pump-probe measurements
Rayleigh and Raman scattering and IR absorption
Semiconductor laser
Tachyons and superluminal motion

Plasma Physics

Alfven wave
Ball lightning
Charge-density wave
Drude model
Dynamos, homogeneous
Electron beam devices
Magnetohydrodynamics
Nonlinear plasma waves
Particle accelerators
Plasma soliton experiments

Social Science

Economic dynamics
Epidemiology
Game theory
Hierarchies of nonlinear systems
Population dynamics
Traffic flow

Solid Mechanics and Nonlinear Vibrations

Angle of repose
Avalanche breakdown
Bilayer lipid membranes
Bjerrum defects
Charge-density wave
Cluster coagulation
Color centers
Detailed balance
Dislocations in crystals
Domain walls
Frustration
Glacial flow
Granular media
Growth patterns
Heat conduction
Hydrogen bond
Ising model
Kerr effect
Langmuir-Blodgett films
Liquid crystals
Local modes in molecular crystals
Mechanics of solids
Molecular dynamics
Nonlinear acoustics
Protein dynamics
Ratchets
Rheology
Sandpile model
Scheibe aggregates
Shock waves
Spin systems
Superlattices
Tessellation
Topological defects

Theoretical Physics

Berry's phase
Black holes
Born-Infeld equation
Celestial mechanics
Cherenkov radiation
Conervation laws and constants of motion
Cosmological models
Critical phenomena
Derrick-Hobart theorem
Detailed balance
Einstein equations
Entropy
Equipartition of energy
Fluctuation-dissipation theorem
Fokker-Planck equation
Free energy
Galaxies
General relativity
Gravitational waves
Hamiltonian systems
Higgs boson
Instantons
N-body problem
Newton's laws of motion
Matter, nonlinear theory of
Particles and antiparticles
Quantum field theory
Quantum theory
Regular and chaotic dynamics in atomic physics
Rotating rigid bodies
Skyrmions
String theory
Tachyons and superluminal motion
Twistor theory
Virial theorem
Yang-Mills theory