Statics and Dynamics of Nonlinear Systems

1 Basic Aspects of Nonlinear Systems.- 1.1 Introduction.- 1.2 Spectral Transform and Solitons.- 1.3 Linear and Nonlinear Aspects in Lattice Dynamics.- 1.4 The Thermoelastic-Plastic Transition in Metals: Thermal Emission as a Probe to Identify the Yield Point.- 1.5 Solvable Many-Body Problems.- 1.6 Stability of Hydrated M1+-DNAs: A Challenge in the Theory of Nonlinear Systems.- 2 Phase Transitions.- 2.1 Anharmonic Properties Near Structural Phase Transitions: An Update.- 2.2 Critical Phenomena from Wilson's Exact Renormalization-Group Equation.- 2.3 Quantum Fluctuations of a 3-Dimensional ?4 Model-Quantum Ferroelectrics.- 2.4 Stochastic Quantization and Critical Dynamics.- 3 Incommensurate Phases and Charge-Density Waves.- 3.1 The Physical Mechanisms Leading to Incommensurate Phases.- 3.2 Excitations and Chaotic States in Incommensurate Multi-Soliton Lattices: Experiments.- 3.3 The Transition by Breaking of Analyticity in Incommensurate Structures and the Devil's Staircase; Application to Metal-Insulator Transitions in Peierls Chains.- 3.4 Non-Linearity Induced by Charge-Density Wave Motion.- 3.5 Low-Frequency Dynamics of Soliton Lattices.- 4 Chaos in Condensed Matter.- 4.1 Universality and Fractal Dimension of Mode-Locking Structure in Systems with Competing Periodicities.- 4.2 Chaos and Solitons in Josephson Junctions.- 4.3 Transition to Deterministic Chaos in a Hydrodynamic System.- 4.4 Chaos and Solitons in Dissipative Nonlinear Systems.- 4.5 Chaos-Induced Diffusion.- 5 Solitons and Other Exact Solutions of Nonlinear Equations.- 5.1 Classical Statistical Mechanics of Lattice Dynamic Model Systems: Transfer Integral and Molecular-Dynamics Studies.- 5.2 The Spectral Transform: Methods for the Fourier Analysis of Nonlinear Wave Data.- 5.3 Kink- and Polaron-Solitonsin Models of Polyacetylene and Other Peierls-Distorted Materials.- 5.4 Counting Solitons and Phonons in the Toda Lattice.- 5.5 Structure of Interfaces.- 5.6 Commensurate Structures in Solids.- 5.7 Periodon Solutions in Two- and Three-Dimensional Lattices.- 5.8 Intrinsic Non-Linearity (in Phonon Numbers) of the Response Functions of Elastic Systems: A Proposal of Quantum Acoustics.- Index of Contributors.