ABSTRACT
In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
TABLE OF CONTENTS
letter 1|35 pages
A
entry |1 pages
AB Initio Calculations
entry |2 pages
Ablowitz-Kaup-Newell-Segur System
entry |1 pages
Ablowitz–Ladik Equation
entry |1 pages
Acoustic Solitons
entry |1 pages
Action Potential
entry |1 pages
Action-Angle Variables
entry |1 pages
Activator-Inhibitor System
entry |1 pages
Adiabatic Approximation
entry |3 pages
Adiabatic Invariants
entry |3 pages
Alfvén Waves
entry |3 pages
Algorithmic Complexity
entry |1 pages
All-or-Nothing Response
entry |1 pages
Almost Periodic Functions
entry |1 pages
Ambiguous Figures
entry |3 pages
Anderson Localization
entry |1 pages
Annihilation (Kink-Antikink)
entry |3 pages
Anosov and Axiom-A Systems
entry |1 pages
Antisolitons
entry |1 pages
Anti-Stokes Scattering
entry |1 pages
Arnol'd Cat Map
entry |3 pages
Arnol'd Diffusion
entry |1 pages
Arnol'd Tongues
entry |3 pages
Artificial Intelligence
entry |2 pages
Artificial Life
entry |1 pages
Assembly of Neurons
entry |8 pages
Atmospheric and Ocean Sciences
entry |2 pages
Attractor Neural Networks
entry |3 pages
Attractors
entry |3 pages
Aubry-Mather Theory
entry |1 pages
Auto-Bäcklund Transformation
entry |1 pages
Autocatalytic System
entry |1 pages
Autocorrelation Function
entry |1 pages
Autonomous System
entry |1 pages
Auto-Oscillations
entry |3 pages
Avalanche Breakdown
entry |3 pages
Avalanches
entry |2 pages
Averaging Methods
letter 2|50 pages
B
entry |3 pages
Bäcklund Transformations
entry |1 pages
Baker Map
entry |1 pages
Baker–Akhiezer Function
entry |4 pages
Ball Lightning
entry |1 pages
Banach Space
entry |1 pages
Basin of Attraction
entry |1 pages
Baxter's Q-Operator
entry |3 pages
Belousov–Zhabotinsky Reaction
entry |1 pages
Benjamin–Bona–Mahony Equation
entry |1 pages
Benjamin–Feir Instability
entry |1 pages
Benjamin–Ono Equation
entry |1 pages
Bernoulli Shift
entry |2 pages
Bernoulli's Equation
entry |3 pages
Berry's Phase
entry |3 pages
Bethe Ansatz
entry |3 pages
Bifurcations
entry |1 pages
Bi-Hamiltonian Structure
entry |3 pages
Bilayer Lipid Membranes
entry |3 pages
Billiards
entry |3 pages
Binding Energy
entry |4 pages
Biological Evolution
entry |5 pages
Biomolecular Solitons
entry |1 pages
Bions
entry |1 pages
Birge–Sponer Relation
entry |1 pages
Birkoff–Smale Theorem
entry |1 pages
Bistability
entry |1 pages
Bistable Equation
entry |2 pages
Bjerrum Defects
entry |3 pages
Black Holes
entry |1 pages
Bloch Domainwall
entry |1 pages
Bloch Functions
entry |1 pages
Blowout Bifurcation
entry |1 pages
Blow-Up (Collapse)
entry |1 pages
Bohr–Sommerfeld Quantization
entry |1 pages
Boomerons
entry |3 pages
Born–Infeld Equations
entry |3 pages
Bose–Einstein Condensation
entry |1 pages
Bosons
entry |2 pages
Boundary Layers
entry |3 pages
Boundary Value Problems
entry |1 pages
Boussinesq Equations
entry |1 pages
Box Counting
entry |1 pages
Brain Waves
entry |2 pages
Branching Laws
entry |3 pages
Breathers
entry |1 pages
Brouwer'S Fixed Point Theorem
entry |4 pages
Brownian Motion
entry |2 pages
Brusselator
entry |1 pages
Bullets
entry |3 pages
Burgers Equation
entry |3 pages
Butterfly Effect
letter 3|96 pages
C
entry |1 pages
Calogero–Moser Model
entry |2 pages
Candle
entry |1 pages
Canonical Variables
entry |1 pages
Cantor Sets
entry |1 pages
Capacity Dimension
entry |1 pages
Capillary Waves
entry |3 pages
Cardiac Arrhythmias and the Electrocardiogram
entry |5 pages
Cardiac Muscle Models
entry |1 pages
Casimirs
entry |3 pages
Cat Map
entry |3 pages
Catalytic Hypercycle
entry |2 pages
Catastrophe Theory
entry |3 pages
Causality
entry |1 pages
Caustics
entry |1 pages
Cavity Solitons
entry |2 pages
Celestial Mechanics
entry |3 pages
Cell Assemblies
entry |3 pages
Cellular Automata
entry |5 pages
Cellular Nonlinear Networks
entry |4 pages
Center Manifold Reduction
entry |1 pages
Central Limit Theorem
entry |4 pages
Chaos Vs. Turbulence
entry |2 pages
Chaotic Advection
entry |1 pages
Chaotic Billiards
entry |11 pages
Chaotic Dynamics
entry |4 pages
Characteristics
entry |3 pages
Charge Density Waves
entry |3 pages
Chemical Kinetics
entry |2 pages
Cherenkov Radiation
entry |1 pages
Chi(2) Materials and Solitons
entry |1 pages
Chirikov Map
entry |3 pages
Chua's Circuit
entry |1 pages
Circle Map
entry |4 pages
Clear Air Turbulence
entry |4 pages
Cluster Coagulation
entry |1 pages
Cnoidal Wave
entry |4 pages
Coherence Phenomena
entry |1 pages
Coherent Exciton
entry |1 pages
Coherent Structures
entry |1 pages
Cole-Hopf Transform
entry |1 pages
Collapse
entry |2 pages
Collective Coordinates
entry |3 pages
Collisions
entry |3 pages
Color Centers
entry |4 pages
Commensurate-Incommensurate Transition
entry |1 pages
Compact Set
entry |1 pages
Compacton
entry |3 pages
Compartmental Models
entry |4 pages
Complex Ginzburg–Landau Equation
entry |1 pages
Complexity, Measures of
entry |1 pages
Condensates
entry |3 pages
Conley Index
entry |5 pages
Constants of Motion and Conservation Laws
entry |1 pages
Continuity Equation
entry |1 pages
Continuous Spectrum
entry |3 pages
Continuum Approximations
entry |4 pages
Contour Dynamics
entry |1 pages
Control Parameters
entry |3 pages
Controlling Chaos
entry |2 pages
Cosmological Models
entry |1 pages
Convection
entry |1 pages
Convective Instablity
entry |1 pages
Correlation Dimension
entry |1 pages
Correspondence Principle
entry |2 pages
Coupled Map Lattice
entry |2 pages
Coupled Oscillators
entry |3 pages
Coupled Systems of Partial Differential Equations
entry |4 pages
Critical Phenomena
entry |1 pages
Critical Points
entry |1 pages
Crystal Dislocations
entry |1 pages
Crystals, Molecular
entry |1 pages
Cubic Map
letter 4|61 pages
D
entry |3 pages
Damped-Driven Anharmonic Oscillator
entry |3 pages
Darboux Transformation
entry |1 pages
Davey-Stewartson Equation
entry |3 pages
Davydov Soliton
entry |1 pages
Delay Coordinates
entry |3 pages
Delay-Differential Equations
entry |3 pages
Denjoy Theory
entry |1 pages
Derivative NLS Equation
entry |2 pages
Derrick–Hobart Theorem
entry |3 pages
Detailed Balance
entry |3 pages
Determinism
entry |3 pages
Deterministic Walks in Random Environments
entry |3 pages
Development of Singularities
entry |1 pages
Devil's Staircase
entry |1 pages
Diffeomorphism
entry |3 pages
Differential Geometry
entry |3 pages
Diffusion
entry |3 pages
Dimensional Analysis
entry |3 pages
Dimensions
entry |2 pages
Diodes
entry |1 pages
Dirac's Delta Function
entry |3 pages
Discrete Breathers
entry |3 pages
Discrete Nonlinear Schrödinger Equations
entry |3 pages
Discrete Self-Trapping System
entry |3 pages
Dislocations in Crystals
entry |4 pages
Dispersion Management
entry |2 pages
Dispersion Relations
entry |3 pages
Distributed Oscillators
entry |3 pages
DNA Premelting
entry |3 pages
DNA Solitons
entry |2 pages
Domain Walls
entry |2 pages
Doppler Shift
entry |1 pages
Double-Well Potential
entry |3 pages
Dressing Method
entry |3 pages
Dripping Faucet
entry |2 pages
Drude Model
entry |3 pages
Duffing Equation
entry |3 pages
Dune Formation
entry |1 pages
Dym Equation
entry |1 pages
Dynamic Pattern Formation
entry |1 pages
Dynamic Scaling function
entry |2 pages
Dynamical Systems
entry |1 pages
Dynamical Zeta Functions
entry |3 pages
Dynamos, Homogeneous
letter 5|46 pages
E
entry |1 pages
Earthquakes
entry |1 pages
Eckhaus Instability
entry |4 pages
Economic System Dynamics
entry |2 pages
Effective Mass
entry |1 pages
Eiffel Junction
entry |1 pages
Eigenvalues and Eigenvectors (Bound State)
entry |1 pages
Eikonal Curvature Equation
entry |2 pages
Einstein Equations
entry |1 pages
Elastic and Inelastic Collisions
entry |3 pages
Electroencephalogram at Large Scales
entry |3 pages
Electroencephalogram at Mesoscopic Scales
entry |3 pages
Electron Beam Microwave Devices
entry |3 pages
Elliptic Functions
entry |2 pages
Embedding Methods
entry |2 pages
Emergence
entry |1 pages
Endomorphism
entry |3 pages
Energy Analysis
entry |1 pages
Energy Cascade
entry |1 pages
Energy Operators
entry |1 pages
Entrainment
entry |3 pages
Entropy
entry |1 pages
Envelope Equations
entry |1 pages
Envelope Solitons
entry |2 pages
Ephaptic Coupling
entry |3 pages
Epidemiology
entry |3 pages
Equations, Nonlinear
entry |3 pages
Equilibrium
entry |3 pages
Equipartition of Energy
entry |2 pages
Ergodic Theory
entry |1 pages
Esaki Tunnel Diode
entry |1 pages
Euler's Method
entry |1 pages
Eulerian Description
entry |2 pages
Euler-Lagrange Equations
entry |2 pages
Evans function
entry |5 pages
Evaporation Wave
entry |2 pages
Excitability
entry |1 pages
Excitable Medium
entry |2 pages
Excitons
entry |3 pages
Explosions
entry |3 pages
Extremum Principles
letter 6|59 pages
F
entry |1 pages
Fabry–Perot Resonances
entry |2 pages
Fairy Rings of Mushrooms
entry |1 pages
Faraday Waves
entry |3 pages
Feedback
entry |1 pages
Feigenbaum Theory
entry |3 pages
Fermi Acceleration and Fermi Map
entry |1 pages
Fermi Resonance
entry |4 pages
Fermi–Pasta–Ulam Oscillator Chain
entry |3 pages
Ferromagnetism and Ferroelectricity
entry |1 pages
Fibers, Optical
entry |2 pages
Fibonacci Series
entry |1 pages
Fibrillation
entry |4 pages
Filamentation
entry |1 pages
Fingering
entry |1 pages
Finite Element Methods
entry |1 pages
Finite-Difference Methods
entry |1 pages
Fisher's Equation
entry |1 pages
Fiske Steps
entry |3 pages
Fitness Landscape
entry |2 pages
Fitzhugh–Nagumo Equation
entry |1 pages
Fixed Points
entry |4 pages
Flame Front
entry |2 pages
Flip-Flop Circuit
entry |1 pages
Floquet Theory
entry |3 pages
Fluctuation-Dissipation Theorem
entry |5 pages
Fluid Dynamics
entry |1 pages
Flux Flow Oscillator
entry |1 pages
Flux Quantization
entry |1 pages
Fluxon
entry |1 pages
Focusing System
entry |3 pages
Fokker–Planck Equation
entry |1 pages
Forced Systems
entry |2 pages
Forecasting
entry |3 pages
Forest Fires
entry |1 pages
Fourier Transform
entry |1 pages
Four-Wave Mixing
entry |1 pages
Fractal Dimension
entry |5 pages
Fractals
entry |3 pages
Framed Space Curves
entry |2 pages
Franck–Condon Factor
entry |2 pages
Fredholm Theorem
entry |3 pages
Free Energy
entry |2 pages
Free Probability Theory
entry |4 pages
Frenkel–Kontorova Model
entry |3 pages
Frequency Doubling
entry |1 pages
Frequency Locking
entry |3 pages
Fröhlich Theory
entry |1 pages
Front Propagation
entry |3 pages
Frustration
entry |3 pages
Function Spaces
entry |3 pages
Functional Analysis
letter 7|40 pages
G
entry |2 pages
Galaxies
entry |3 pages
Game of Life
entry |2 pages
Game Theory
entry |1 pages
Gap Solitons
entry |1 pages
Gardner (GGKM) Equation
entry |1 pages
Gaussian Beam
entry |1 pages
Gaussian Ensembles
entry |4 pages
Gel'fand-Levitan Theory
entry |3 pages
General Circulation Models of the Atmosphere
entry |3 pages
General Relativity
entry |3 pages
Generalized Functions
entry |4 pages
Geometrical Optics, Nonlinear
entry |3 pages
Geomorphology and Tectonics
entry |3 pages
Gestalt Phenomena
entry |1 pages
Ginzburg–Landau Equation
entry |3 pages
Glacial Flow
entry |5 pages
Global Warming
entry |1 pages
Golden Mean
entry |4 pages
Gradient System
entry |3 pages
Granular Materials
entry |3 pages
Gravitational Waves
entry |1 pages
Gravity Waves
entry |1 pages
Green's Function
entry |1 pages
Grey Soliton
entry |1 pages
Gross-Pitaevskii Equation
entry |4 pages
Group Velocity
entry |3 pages
Growth Patterns
entry |1 pages
Gutzwiller Trace Formula
letter 8|47 pages
H
entry |4 pages
Hamiltonian Systems
entry |3 pages
Harmonic Generation
entry |1 pages
Harmonic Oscillators
entry |3 pages
Hartree Approximation
entry |1 pages
Hausdorff Dimensio
entry |3 pages
Heat Conduction
entry |1 pages
Heaviside Step Function
entry |2 pages
Hele-Shaw Cell
entry |1 pages
Helical Waves
entry |3 pages
Helicity
entry |4 pages
Hénon Map
entry |3 pages
Hénon–Heiles System
entry |1 pages
Heteroclinic Intersection
entry |1 pages
Heteroclinic Trajectory
entry |2 pages
Hierarchies of Nonlinear Systems
entry |2 pages
Higgs Boson
entry |1 pages
Hill's Equation
entry |3 pages
Hirota's Method
entry |3 pages
Hodgkin–Huxley Equations
entry |3 pages
Hodograph Transform
entry |3 pages
Hole Burning
entry |2 pages
Holons
entry |1 pages
Holstein Model
entry |1 pages
Holstein–Primakov Transformation
entry |1 pages
Homeomorphism
entry |1 pages
Homoclinic Intersection
entry |1 pages
Homoclinic Trajectory
entry |4 pages
Hopf Bifurcation
entry |1 pages
Hopfield Model
entry |4 pages
Horseshoes and Hyperbolicity in Dynamical Systems
entry |3 pages
Hurricanes and Tornadoes
entry |2 pages
Huygens Principle
entry |1 pages
Hydraulic Jumps
entry |1 pages
Hydrodynamic Limit
entry |1 pages
Hydrodynamic Solitary Waves
entry |2 pages
Hydrogen Bond
entry |4 pages
Hydrothermal Waves
entry |1 pages
Hyperbolic Mappings
entry |1 pages
Hyperchaos
entry |1 pages
Hypercycle
entry |1 pages
Hyperelleptic Functions
entry |3 pages
Hysteresis
letter 9|39 pages
I
entry |3 pages
Idempotent Analysis
entry |1 pages
Ikeda Map
entry |1 pages
Impulse, Nerve
entry |3 pages
Incoherent Solitons
entry |2 pages
Inertial Manifolds
entry |1 pages
Infeld Equation
entry |1 pages
Information Dimension
entry |3 pages
Information Theory
entry |3 pages
Inhibition
entry |2 pages
Instability
entry |4 pages
Integrability
entry |4 pages
Integrable Cellular Automata
entry |5 pages
Integrable Lattices
entry |1 pages
Integrable Tops
entry |1 pages
Integral Equations
entry |3 pages
Integral Transforms
entry |1 pages
Integrals of Motion
entry |2 pages
Integrate and Fire Neuron
entry |1 pages
Integro-Differential Equations
entry |3 pages
Intermittency
entry |3 pages
Invariant Manifolds and Sets
entry |1 pages
Invariant Measure
entry |4 pages
Inverse Problems
entry |6 pages
Inverse Scattering Method or Transform
entry |1 pages
Ion Acoustic Waves
entry |2 pages
Ising Model
entry |1 pages
Ito's Formula
entry |1 pages
Izergin-Korepin Equation
letter 10|10 pages
J
entry |1 pages
Jacobi Elliptic Functions
entry |2 pages
Josephson Junction Arrays
entry |4 pages
Josephson Junctions
entry |1 pages
Jost Functions
entry |1 pages
Julia Sets
entry |4 pages
Jump Phenomena
entry |3 pages
Jupiter's Great Red Spot
letter 11|24 pages
K
entry |3 pages
Kadomtsev-Petviashvili Equation
entry |3 pages
Kelvin–Helmholtz Instability
entry |1 pages
Kepler Problem
entry |1 pages
K-Epsilon Method
entry |1 pages
Kermack–Mckendrick System
entry |3 pages
Kerr Effect
entry |3 pages
Kicked Rotor
entry |1 pages
Kinks and Antikinks
entry |2 pages
Kirchhoff's Laws
entry |1 pages
Klein–Gordon Equation
entry |4 pages
Knot Theory
entry |1 pages
Koch Curve
entry |3 pages
Kolmogorov Cascade
entry |1 pages
Kolmogorov, Petrovsky and Piscounoff Equation
entry |2 pages
Kolmogorov–Arnol'd–Moser Theorem
entry |8 pages
Korteweg–de Vries Equation
entry |1 pages
Krylov–Bogolyubov Method
entry |2 pages
Kuramoto–Sivashinsky Equation
letter 12|31 pages
L
entry |3 pages
Laboratory Models of Nonlinear Waves
entry |1 pages
Lagrange–Euler Equations
entry |1 pages
Lagrangian Description
entry |1 pages
Lamb Diagram
entry |1 pages
Landau Equation
entry |3 pages
Landau–Lifshitz Equation
entry |1 pages
Langevin Equation
entry |1 pages
Langmuir Waves
entry |4 pages
Langmuir–Blodgett Films
entry |1 pages
Laplace Transform
entry |3 pages
Lasers
entry |3 pages
Lattice Gas Methods
entry |1 pages
Lattice Kink
entry |1 pages
Lattice Solitons
entry |1 pages
Lax Operators
entry |1 pages
Leading Edge Dynamics
entry |1 pages
Lebesque Measure
entry |1 pages
Legendre Transformation
entry |1 pages
Lennard–Jones Potential
entry |3 pages
Lévy Flights
entry |3 pages
Lie Algebras And Lie Groups
entry |2 pages
Lifetime
entry |1 pages
Lighthill Criterion
entry |1 pages
Lindstedt–Poincaré Method
entry |2 pages
Linearization
entry |1 pages
Liouville Equation
entry |1 pages
Liouville Theorem
entry |1 pages
Lipschitz Condition
entry |3 pages
Liquid Crystals
entry |3 pages
Local Modes in Molecular Crystals
entry |2 pages
Local Modes in Molecules
entry |1 pages
Localization
entry |1 pages
Locking
entry |1 pages
Logic, Dendritic
entry |1 pages
Logistic Equation
entry |1 pages
Logistic Map
entry |2 pages
Long Josephson Junctions
entry |1 pages
Long Water Wave Approximations
entry |1 pages
Long-Wavelength Approximation
entry |1 pages
Loop Solitons
entry |1 pages
Loop, Closed Causal
entry |3 pages
Lorentz Gas
entry |1 pages
Lorentz Transform
entry |1 pages
Lorenz Attractor
entry |3 pages
Lorenz Equations
entry |1 pages
Lotka–Volterra Equations
entry |2 pages
Lyapunov Exponents
entry |1 pages
Lyapunov Stability
letter 13|59 pages
M
entry |1 pages
Mach Stem Effect
entry |2 pages
Magnetohydrodynamics
entry |1 pages
Manakov Equations
entry |1 pages
Mandelbrot Sets
entry |2 pages
Manley–Rowe Relations
entry |6 pages
Maps
entry |3 pages
Maps in the Complex Plane
entry |1 pages
Marangoni Convection
entry |1 pages
Marginal Stability
entry |2 pages
Markin–Chizmadzhev Model
entry |1 pages
Markov Chain
entry |3 pages
Markov Partitions
entry |4 pages
Martingales
entry |1 pages
Mathieu Equation
entry |2 pages
Matter, Nonlinear Theory of
entry |3 pages
Maxwell–Bloch Equations
entry |2 pages
Mcculloch–Pitts Network
entry |1 pages
Mean Field Theories
entry |2 pages
Measures
entry |3 pages
Mechanics of Solids
entry |3 pages
Mel'nikov Method
entry |1 pages
Metastability
entry |1 pages
Meteorology
entry |1 pages
Missing Mass (For KDV Soliton)
entry |1 pages
Miura Transformation
entry |3 pages
Mixing
entry |1 pages
Möbius Strip
entry |1 pages
Mode Locking
entry |1 pages
Mode Mixing and Coupling
entry |1 pages
Modified KDV Equation
entry |3 pages
Modulated Waves
entry |1 pages
Modulational Instability
entry |1 pages
Molecular Crystals
entry |6 pages
Molecular Dynamics
entry |5 pages
Monodromy Preserving Deformations
entry |3 pages
Monte Carlo Methods
entry |3 pages
Morphogenesis, Biological
entry |2 pages
Multidimensional Solitons
entry |3 pages
Multifractal Analysis
entry |1 pages
Multifractal Measure
entry |2 pages
Multiple Scale Analysis
entry |3 pages
Multiplex Neuron
entry |1 pages
Multiplicative Noise
entry |5 pages
Multiplicative Processes
entry |3 pages
Multisoliton Perturbation Theory
entry |1 pages
Multistability
entry |1 pages
Mushrooms
entry |1 pages
Mutual Entrainment
entry |2 pages
Myelinated Nerves
letter 14|59 pages
N
entry |1 pages
Natural Measure
entry |4 pages
Navier–Stokes Equation
entry |3 pages
N-Body Problem
entry |1 pages
Neel Domain Wall
entry |1 pages
Negative Resistance and Conductance
entry |3 pages
Nephron Dynamics
entry |3 pages
Nerve Impulses
entry |1 pages
Neumann Boundary Condition
entry |3 pages
Neural Network Models
entry |3 pages
Neuristor
entry |3 pages
Neurons
entry |1 pages
Newell–Whitehead–Segel Equation
entry |2 pages
Newton's Laws of Motion
entry |1 pages
Newton's Method
entry |1 pages
Nodes of Ranvier
entry |1 pages
Noise (White, Colored Etc.)
entry |1 pages
Nonattracting Chaotic Sets
entry |1 pages
Nonautonomous Systems
entry |5 pages
Nonequilibrium Statistical Mechanics
entry |1 pages
Nonergodicity
entry |1 pages
Nonintegrable Lattices
entry |2 pages
Nonlinear Acoustics
entry |3 pages
Nonlinear Electronics
entry |8 pages
Nonlinear Optics
entry |5 pages
Nonlinear Plasma Waves
entry |1 pages
Nonlinear Resonance
entry |5 pages
Nonlinear Schrödinger Equations
entry |3 pages
Nonlinear Signal Processing
entry |1 pages
Nonlinear Superposition
entry |3 pages
Nonlinear Toys
entry |1 pages
Nonlinear Transparency
entry |3 pages
Nonlinearity, Definition of
entry |1 pages
Non-Newtonian Fluids
entry |1 pages
Non-Topological Soliton
entry |3 pages
Nontwist Maps
entry |3 pages
Normal Forms Theory
entry |3 pages
N-Soliton Formulas
entry |1 pages
N-Tori
entry |7 pages
Numerical Methods
entry |2 pages
N-Wave Interactions
letter 15|14 pages
O
entry |4 pages
One-Dimensional Maps
entry |1 pages
Open Sets
entry |3 pages
Optical Fiber Communications
entry |1 pages
Optical Nonlinearities
entry |1 pages
Orbit
entry |3 pages
Order From Chaos
entry |3 pages
Order Parameters
entry |3 pages
Ordinary Differential Equations, Nonlinear
entry |1 pages
Organizing Centers
entry |1 pages
Oscillator, Classical Nonlinear
entry |3 pages
Overtones
letter 16|70 pages
P
entry |4 pages
Painlevé Analysis
entry |2 pages
Parametric Amplification
entry |1 pages
Parametric Decay Instability
entry |3 pages
Partial Differential Equations, Nonlinear
entry |4 pages
Particle accelerators
entry |3 pages
Particles And Antiparticles
entry |4 pages
Pattern Formation
entry |1 pages
Pattern Selection
entry |3 pages
Peierls Barrier
entry |2 pages
Pendulum
entry |3 pages
Perceptron
entry |3 pages
Percolation Theory
entry |3 pages
Period Doubling
entry |2 pages
Periodic Bursting
entry |3 pages
Periodic Orbit Theory
entry |4 pages
Periodic Spectral Theory
entry |1 pages
Permanent Wave
entry |3 pages
Perturbation Theory
entry |2 pages
Phase Dynamics
entry |1 pages
Phase Locking
entry |1 pages
Phase Matching
entry |3 pages
Phase Plane
entry |4 pages
Phase Space
entry |2 pages
Phase-Space Diffusion and Correlations
entry |1 pages
Phase Space Reconstruction
entry |1 pages
Phase Synchronism of Chaos
entry |2 pages
Phase Transitions
entry |1 pages
Phase Turbulence
entry |1 pages
Phase Winding
entry |1 pages
Phi-Four Equation
entry |3 pages
Photonic Crystals
entry |1 pages
Piecewise Linearity
entry |1 pages
Pinning to Lattice
entry |1 pages
Pitchfork Bifurcation
entry |2 pages
Plasma Soliton Experiments
entry |1 pages
Plasma Turbulence
entry |1 pages
Plastic Deformation
entry |4 pages
Plume Dynamics
entry |1 pages
Poincaré Index
entry |2 pages
Poincaré Theorems
entry |1 pages
Poincaré–Bendixson Theorem
entry |2 pages
Poisson Brackets
entry |4 pages
Polaritons
entry |3 pages
Polarons
entry |3 pages
Polymerization
entry |4 pages
Population Dynamics
entry |3 pages
Power Balance
entry |1 pages
Power Spectra
entry |1 pages
Prandtl Number
entry |1 pages
Predator-Prey Systems
entry |1 pages
Predictability of forecasting
entry |3 pages
Protein Dynamics
entry |2 pages
Protein Structure
entry |1 pages
Pseudo-Differential Equations
entry |1 pages
Pulsons
entry |3 pages
Pump-Probe Measurements
letter 17|16 pages
Q
entry |1 pages
Q-Deformation
entry |1 pages
Quadratic Family
entry |1 pages
Quantum Billiards
entry |3 pages
Quantum Chaos
entry |4 pages
Quantum Field Theory
entry |2 pages
Quantum Inverse Scattering Method
entry |4 pages
Quantum Nonlinearity
entry |3 pages
Quantum Theory
entry |3 pages
Quasilinear Analysis
entry |3 pages
Quasiperiodicity
letter 18|53 pages
R
entry |1 pages
Raman Solitons
entry |3 pages
Random Matrix Theory I: Origins and Physical Applications
entry |2 pages
Random Matrix Theory II: Algebraic Developments
entry |3 pages
Random Matrix Theory III: Combinatorics
entry |5 pages
Random Matrix Theory Iv: Analytic Methods
entry |1 pages
Random Processes
entry |3 pages
Random Walks
entry |4 pages
Ratchets
entry |3 pages
Rayleigh and Raman Scattering and IR Absorption
entry |1 pages
Rayleigh–Bénard Convection
entry |2 pages
Rayleigh–Taylor Instability
entry |7 pages
Reaction-Diffusion Systems
entry |4 pages
Recurrence
entry |5 pages
Regular and Chaotic Dynamics in Atomic Physics
entry |3 pages
Relaxation Oscillators
entry |3 pages
Renormalization Groups
entry |1 pages
Reynolds Number
entry |3 pages
Rheology
entry |3 pages
Riccati Equations
entry |1 pages
Riemann Invariants
entry |1 pages
Riemann Surfaces
entry |1 pages
Riemann Wave
entry |1 pages
Riemann Zeta function
entry |5 pages
Riemann–Hilbert Problem
entry |1 pages
Ring Solitons
entry |1 pages
Robustness
entry |1 pages
Rossby Waves
entry |4 pages
Rössler Systems
entry |3 pages
Rotating Rigid Bodies
entry |2 pages
Rotating Wave Approximation
entry |1 pages
Rotation-Modified Kortweg-De Vries Equation
entry |4 pages
Routes to Chaos
entry |1 pages
Ruelle–Takens–Newhouse
entry |1 pages
Runge–Kutta Method
letter 19|96 pages
S
entry |1 pages
Saddle Point
entry |1 pages
Saffman–Taylor Problem
entry |3 pages
Salerno Equation
entry |3 pages
Sandpile Model
entry |1 pages
Scattering Operators
entry |2 pages
Scheibe Aggregates
entry |1 pages
Schlesinger Equations
entry |1 pages
Schottky Diode
entry |1 pages
Schrödinger Equation, Linear
entry |3 pages
Scroll Waves
entry |1 pages
Second Harmonic Generation
entry |1 pages
Self-Organization
entry |1 pages
Self-Similarity
entry |1 pages
Semiclassical Approximations
entry |4 pages
Semiconductor Laser
entry |3 pages
Semiconductor Oscillators
entry |1 pages
Semi-Linear Pdes
entry |1 pages
Sensitive Dependence on Initial Conditions
entry |2 pages
Separation of Variables
entry |1 pages
Separatrix
entry |1 pages
Shapiro Steps
entry |1 pages
Sharkovsky's Theorem
entry |3 pages
Shear Flows
entry |3 pages
Shock Waves
entry |1 pages
Shooting Method
entry |1 pages
Sierpinski Gasket
entry |1 pages
Signaling Problem
entry |1 pages
Sinai Billiard
entry |3 pages
Sinai–Ruelle–Bowen Measures
entry |4 pages
Sine-Gordon Equation
entry |1 pages
Singular Perturbation Theory
entry |1 pages
Singular Points
entry |3 pages
Singularity Theory
entry |1 pages
Sink
entry |1 pages
S-Integrability and C-Integrability
entry |4 pages
Skyrmions
entry |1 pages
Slaving Principle
entry |1 pages
Smale Horseshoe
entry |1 pages
Snowflakes
entry |2 pages
Solar System
entry |1 pages
Solidification Patterns
entry |1 pages
Soliton Wave Packet
entry |4 pages
Solitons
entry |4 pages
Solitons, a Brief History
entry |6 pages
Solitons, Types of
entry |1 pages
Solution Trajectory
entry |4 pages
Spatiotemporal Chaos
entry |2 pages
Spectral Analysis
entry |3 pages
Spin Systems
entry |3 pages
Spiral Waves
entry |3 pages
Stability
entry |1 pages
Stable and Unstable Mainfolds
entry |4 pages
Standard Map
entry |2 pages
State Diagrams
entry |1 pages
Stationary Solutions
entry |1 pages
Steady State
entry |4 pages
Stereoscopic Vision and Binocular Rivalry
entry |1 pages
Stimulated Brillouinand Raman Scattering
entry |5 pages
Stochastic Analysis of Neural Systems
entry |3 pages
Stochastic Processes
entry |1 pages
Stokes Scattering
entry |1 pages
Strange Attractors
entry |2 pages
String Theory
entry |1 pages
Strong Collapse
entry |3 pages
Structural Complexity
entry |1 pages
Subharmonic Generation
entry |3 pages
Superconducting Quantum Interference Device
entry |4 pages
Superconductivity
entry |3 pages
Superfluidity
entry |3 pages
Superlattices
entry |1 pages
Supersymmetry
entry |4 pages
Surface Waves
entry |3 pages
Symbolic Dynamics
entry |1 pages
Symmetry Breaking
entry |3 pages
Symmetry Groups
entry |3 pages
Symmetry: Equations Vs. Solutions
entry |3 pages
Symplectic Maps
entry |1 pages
Synapses
entry |3 pages
Synchronization
entry |5 pages
Synergetics
letter 20|48 pages
T
entry |3 pages
Tachyons and Superluminal Motion
entry |2 pages
Tacoma Narrows Bridge Collapse
entry |1 pages
Tangent Space
entry |3 pages
Taylor–Couette Flow
entry |2 pages
Tensors
entry |3 pages
Tessellation
entry |3 pages
Thermal Convection
entry |4 pages
Thermo-Diffusion Effects
entry |2 pages
Theta Functions
entry |1 pages
Three-Body Problem
entry |1 pages
Three-Wave Interaction
entry |3 pages
Threshold Phenomena
entry |3 pages
Time-Series Analysis
entry |7 pages
Toda Lattice
entry |1 pages
Topological Charge
entry |1 pages
Topological Conjugacy
entry |4 pages
Topological Defects
entry |1 pages
Topological Entropy
entry |1 pages
Topological Solitons
entry |3 pages
Topology
entry |4 pages
Traffic Flow
entry |1 pages
Trajectories
entry |1 pages
Transition to Chaos
entry |1 pages
Traveling Wave
entry |1 pages
Triad Interaction
entry |1 pages
Tunnel Diode Arrays
entry |9 pages
Turbulence
entry |3 pages
Turbulence, Ideal
entry |3 pages
Turing Patterns
entry |1 pages
Twist Map
entry |4 pages
Twistor Theory
entry |1 pages
Two Soliton Collision
letter 21|3 pages
U
entry |1 pages
Ueda Equation
entry |3 pages
Universality
entry |1 pages
Unstable Manifold
letter 22|14 pages
V
entry |3 pages
Van Der Pol Equation
entry |1 pages
Vector Field
entry |1 pages
Verhulst Equation
entry |2 pages
Virial Theorem
entry |3 pages
Visiometrics
entry |1 pages
Volcanos
entry |3 pages
Volterra Series and Operators
entry |1 pages
Volterra–Lotka Equations
entry |1 pages
Volume-Preserving Maps
entry |1 pages
Voronoï Diagrams
entry |5 pages
Vortex Dynamics in Excitable Media
entry |3 pages
Vortex Dynamics of Fluids
letter 23|20 pages
W
entry |6 pages
Water Waves
entry |4 pages
Wave of Translation
entry |2 pages
Wave Packets, Linear and Nonlinear
entry |4 pages
Wave Propagation in Disordered Media
entry |4 pages
Wave Stability and Instability
entry |1 pages
Wave Tanks
entry |3 pages
Wavelets
entry |1 pages
Wave Number Selection
entry |1 pages
Weak Collapse
entry |1 pages
Weak Turbulence
entry |1 pages
Weakly Nonlinear Analysis
entry |1 pages
Weather Fronts
entry |1 pages
Weierstrass Elliptic Functions
entry |1 pages
Westervelt Equation
entry |1 pages
Whistlers
entry |1 pages
Whitham's Method
entry |1 pages
Wigner Statistics
entry |3 pages
Winding Numbers
letter 24|2 pages
Y
entry |1 pages
Yang–Baxter Equation
entry |2 pages
Yang–Mills Theory
letter 25|7 pages
Z
entry |1 pages
Zakharov–Shabat Equation
entry |4 pages
Zeldovich–Frank-Kamenetsky Equation
entry |1 pages
Zener Diode
entry |1 pages
Zero Field Steps
entry |4 pages
Zero-Dispersion Limits
entry |1 pages
Zeta Functions