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Index
9 Epilogue
Introduction
1.1 What Is Nonlinear Science?
1.2 An Explosion of Activity
1.3 Causes of the Revolution
2 Chaos
2.1 The Three-Body Problem
2.2 Poincare's Instructive Mistake
2.3 The Lorenz Attractor
2.4 Other Irregular Curves
2.5 The KAM Theorem
2.6 More Early Discoveries of Low-Dimensional Chaos
2.7 Is There Chaos in the Solar System?
3 Solitons
3.2 The Inverse Scattering Method
3.3 The Nonlinear Schrodinger Equation
3.4 The Sine-Gordon Equation
3.5 Nonlinear Lattices
3.6 Some General Comments
4 Nerve Pulses and Reaction-Diffusion Systems
4.2 Simple Nerve Models
4.3 Reaction Diffusion in Higher Dimensions
5 The Unity of Nonlinear Science
5.1.1 Solitons and Reaction Diffusion
5.1.2 The KAM Theorem
5.1.4 Reaction Diffusion and Chaos
5.2 Metatheories of Nonlinear Science
5.2.2 Mathematical Biology (MB)
5.2.3 General Systems Theory (GST)
5.2.4 Nonequilibrium Statistical Mechanics (NSM)
5.2.5 Catastrophe Theory (CT)
5.2.6 Synergetics(S)
5.2.7 Complex Adaptive Systems (CAS)
5.3 Interrelations Among the Metatheories
6 Physical Applications of Nonlinear Theory
6.1.1 Mie's Nonlinear Electromagnetism
6.1.2 De Broglie's Guiding Waves and the Double Solution
6.1.3 Skyrmions
6.1.4 Point vs. Extended Particles
6.2 Quantum Theory
6.2.1 Quantum Probabilities
6.2.2 Schrodinger's Cat
6.2.3 The EPR Paradox
6.2.4 Nonlocality and Quantum Entanglement
6.2.5 Bell's Inequality
6.2.6 Joint Measurability
6.2.7 Many Worlds?
6.2.8 Nonlinear Quantum Mechanics?
6.3 Quantum Energy Localization and Chaos
6.3.2 Quantum Solitons
6.3.3 Quantum Inverse Scattering
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