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.

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