Encyclopedia of Nonlinear Science

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

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

A
Ablowitz-Kaup-Newell-Segur (AKNS) system
Adiabatic invariants
Alfven waves
Algorithmic complexity
Anderson localization
Anosov and Axiom A systems
Arnold diffusion
Artificial intelligence
Artificial life
Atmospheric and ocean sciences
Attractor neural network (ANN)
Attractors
Aubry-Mather theory
Avalanche breakdown
Avalanches
Averaging methods

B
Bäcklund transformations
Ball lightning
Belousov-Zhabotinsky reaction
Bernoulli's equation
Berry's phase
Bethe ansatz
Bifurcations
Bilayer lipid membranes
Billiards
Binding energy
Biological evolution
Biomolecular solitons
Bjerrum defects
Black holes
Born-Infeld equations
Bose-Einstein condensation
Boundary layers
Boundary value problems
Branching laws
Breathers
Brownian motion
Brusselator
Burgers' equation
Butterfly effect

C
Candle
Cardiac arrhythmias and electrocardiogram
Cardiac muscle models
Cat map
Catalytic hypercycle
Catastrophe theory
Causality
Celestial mechanics
Cell assemblies
Cellular automata
Cellular nonlinear networks
Center manifold reduction
Chaos vs. turbulence
Chaotic advection
Chaotic dynamics
Characteristics
Charge density wave
Chemical kinetics
Cherenkov radiation
Chua's circuit
Clear air turbulence
Cluster-cluster coagulation
Coherence phenomena
Collective coordinates
Collisions
Color centers
Commensurate-incommensurate transition
Compartmental models
Complex Ginzburg-Landau (CGL) equation
Conley index
Constants of motion and conservation laws
Continuum approximations
Contour dynamics
Controlling chaos Cosmological models
Coupled map lattice
Coupled oscillators
Coupled systems of partial differential equations
Critical phenomena

D
Damped driven anharmonic oscillator
Darboux transformation
Davydov soliton
Delay-differential equations
Denjoy theory
Derrick-Hobart theorem
Detailed balance
Determinism
Deterministic walks in random environments
Development of singularities
Differential geometry
Diffusion
Dimensional analysis
Dimensions
Diodes
Discrete breathers
Discrete nonlinear Schrödinger equations
Discrete self-trapping system
Dislocations in crystals
Dispersion management
Dispersion relations
Distributed oscillators
DNA premelting
DNA solitons
Domain walls
Doppler shift
Dressing method
Dripping faucet
Drude model
Duffing equation
Dune formation
Dynamical systems
Dynamos, homogeneous

E
Economic system dynamics
Effective mass
Einstein equations
Electroencephalogram at large scales
Electroencephalogram at mesoscopic scales
Electron beam microwave devices
Elliptic functions
Embedding methods
Emergence
Energy analysis
Entropy
Ephaptic coupling
Epidemiology
Equations, nonlinear
Equilibrium
Equipartion of energy
Ergodic theory
Euler-Lagrange equations
Evans function
Evaporation wave
Excitability
Excitons
Explosions
Extremum principles

F
Fairy rings of mushrooms
Feedback
Fermi acceleration and Fermi map
Fermi-Pasta-Ulam (FPU) oscillator chain
Ferromagnetism and ferroelectricity
Fibonacci series
Filamentation
Fitness landscape
FitzHugh-Nagumo equation
Flame front
Flip-flop circuit
Fluctuation-dissipation theorem
Fluid dynamics
Fokker-Planck equation
Forecasting
Forest fires
Fractals
Framed space curves
Franck-Condon factor
Fredholm theorem
Free energy
Free probability theory
Frenkel-Kontorova model
Frequency doubling
Fröhlich theory
Frustration
Function spaces
Functional analysis

G
Galaxies
Game of life
Game theory
Gel'fand-Levitan theory
General circulation models of the atmosphere
General relativity
Generalized functions
Geometrical optics, nonlinear
Geomorphology and tectonics
Gestalt phenomena
Glacial flow
Global warming
Gradient system
Granular materials
Gravitational waves
Group velocity Growth patterns

H
Hénon map
Hénon-Heiles system
Hamiltonian systems
Harmonic generation
Hartree approximation
Heat conduction
Hele-Shaw experiment
Helicity
Hierarchies of nonlinear systems
Higgs boson
Hirota's method
Hodgkin-Huxley equations
Hodograph transform
Hole burning
Holons
Hopf bifurcation
Horseshoes and hyperbolicity in dynamical systems
Hurricanes and tornadoes
Huygens' principle
Hydrogen bond
Hydrothermal waves
Hysteresis

I
Idempotent analysis
Incoherent solitons
Inertial manifolds
Information theory
Inhibition
Instantons
Integrability
Integrable cellular automata
Integrable lattices
Integral transforms
Integrate and fire neuron
Intermittency
Invariant manifolds and sets
Inverse problems
Inverse scattering method or transform
Ising model

J
Josephson junction arrays
Josephson junctions
Jump phenomena
Jupiter's Great Red Spot

K
Kadomtsev-Petviashvili equation
Kelvin-Helmholtz instability
Kerr effect
Kicked rotor
Kirchhoff's laws
Knot theory
Kolmogorov cascade
Kolmogorov-Arnold-Moser theorem
Korteweg-de Vries equation
Kuramoto-Sivashinsky equation

L
Laboratory models of nonlinear waves
Lagrangian chaos
Landau-Lifshitz (LL) equation
Langmuir-Blodgett films
Lasers
Lattice gas methods
Lévy flights
Lie algebras and Lie groups
Lifetime
Linearization
Liquid crystals
Local modes in molecular crystals
Local modes in molecules
Long Josephson junctions
Lorentz gas
Lorenz equations
Lyapunov exponents

M
Magnetohydrodynamics
Manley-Rowe relations
Maps
Maps in the complex plane
Markin-Chizmadzhev model
Markov partitions
Martingales
Matter, nonlinear theory of
Maxwell-Bloch equations
McCulloch-Pitts network
Measures
Mechanics of solids
Melnikov method
Mixing
Modulated waves
Molecular dynamics
Monodromy preserving deformations
Monte Carlo methods
Morphogenesis, biological
Multidimensional solitons
Multifractal analysis
Multiple scale analysis
Multiplex neuron
Multiplicative processes
Multisoliton perturbation theory
Myelinated nerves

N
Navier-Stokes equation
N-body problem
Nephron dynamics
Nerve impulses
Neural network models
Neuristor
Neurons
Newton's laws of motion
Nonequilibrium statistical mechanics
Nonlinear acoustics
Nonlinear electronics
Nonlinear optics
Nonlinear plasma waves
Nonlinear Schrödinger equations
Nonlinear signal processing
Nonlinear toys
Nonlinearity, definition of
Nontwist maps
Normal forms theory
N-soliton formulas
Numerical methods
N-wave interactions

O
One-dimensional maps
Optical fiber communications
Order from chaos
Order parameters
Ordinary differential equations, nonlinear
Overtones

P
Painlevé analysis
Parametric amplification
Partial differential equations, nonlinear
Particle accelerators
Particles and antiparticles
Pattern formation
Peierls barrier
Pendulum
Perceptron
Percolation theory
Period doubling
Periodic bursting
Periodic orbit theory
Periodic spectral theory
Perturbation theory
Phase dynamics
Phase plane
Phase space
Phase space diffusion and correlations
Phase transitions
Photonic crystals
Plasma soliton experiments
Plume dynamics
Poincaré theorems
Poisson brackets
Polaritons
Polarons
Polymerization
Population dynamics
Power balance
Protein dynamics
Protein structure
Pump-probe measurements

Q
Quantum chaos
Quantum field theory
Quantum groups
Quantum inverse scattering method
Quantum nonlinearity
Quantum theory
Quasilinear analysis
Quasiperiodicity

R
Random matrix theory I: origins and physical applications
Random matrix theory II: algebraic developments
Random matrix theory III: combinatorics
Random matrix theory IV: analytic methods
Random walks
Ratchets
Rayleigh and Raman scattering and IR absorption
Rayleigh-Taylor instability
Reaction diffusion systems
Recurrence
Regular and chaotic dynamics in atomic physics
Relaxation oscillators
Renormalization groups
Rheology
Riccati equations
Riemann-Hilbert problem
Rössler systems
Rotating rigid bodies
Rotating wave approximation
Routes to chaos

S
Salerno equation
Sandpile model
Scheibe aggregates
Scroll waves
Semiconductor laser
Semiconductor oscillators
Separation of variables
Shear flow
Shock waves
Sinai-Ruelle-Bowen measures
Sine-Gordon (SG) equation
Singularity theory
Skyrmions
Solar system
Solitons
Solitons, a brief history
Solitons, types of
Spatiotemporal chaos
Spectral analysis
Spin systems
Spiral waves
Stability
Standard map
State diagrams
Stereoscopic Vision and Binocular Rivalry
Stochastic analyses of neural systems
Stochastic processes
String theory
Structural complexity
Superconducting quantum interference device (SQUID)
Superconductivity
Superfluidity
Superlattices
Surface waves
Symbolic dynamics
Symmetry groups
Symmetry: equations vs. solutions
Symplectic maps
Synchronization
Synergetics

T
Tachyons and superluminal motion
Tacoma Narrows Bridge collapse
Taylor-Couette flow
Tensors
Tessellation
Thermal convection
Thermo-diffusion effects
Theta functions
Threshold phenomena
Time series analysis
Toda lattice
Topological defects
Topology
Traffic flow
Turbulence
Turbulence, ideal
Turing patterns
Twistor theory

U
Universality

V
Van der Pol equation
Virial theorem
Visiometrics
Volterra series and operators
Vortex dynamics in excitable media
Vortex dynamics of fluids

W
Water waves
Wave of translation
Wave packets, linear and nonlinear
Wave propagation in disordered media
Wave stability and instability
Wavelets
Winding numbers

Y
Yang-Mills theory

Z
Zeldovich-Frank-Kamenetsky equation
Zero-dispersion limits

A B C D E F G H I J K L M N O P Q R S T U V W Y Z