Ebook: Solitons and Chaos

"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.

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"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.

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"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Integration of Non-Integrable Systems....Pages 3-24
Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions....Pages 25-36
Soliton Dynamics and Chaos Transition in a Microstructured Lattice Model....Pages 37-45
What is the Role of Dynamical Chaos in Irreversible Processes?....Pages 46-57
A Propositional Lattice for the Logic of Temporal Predictions....Pages 58-70
Damping, Quantum Field Theory and Thermodynamics....Pages 71-75
Quasi-Monomial Transformations and Decoupling of Systems of ODE’s....Pages 76-81
Front Matter....Pages 83-83
Solitons in Optical Fibers: First- and Second-Order Perturbations....Pages 85-98
Similarity Solutions of Equations of Nonlinear Optics....Pages 99-107
Heisenberg Ferromagnet, Generalized Coherent States and Nonlinear Behaviour....Pages 108-110
Integrable Supersymmetric Models and Phase Transitions in One Dimension....Pages 111-114
Denaturation of DNA in a Toda Lattice Model....Pages 115-122
Front Matter....Pages 123-123
A Simple Method to Obtain First Integrals of Dynamical Systems....Pages 125-128
Transition to Turbulence in 1-D Rayleigh-B?nard Convection....Pages 129-134
Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow....Pages 135-137
Spatial Coherent Structures in Dissipative Systems....Pages 138-141
Hierarchies of (1+1)-Dimensional Multispeed Discrete Boltzmann Model Equations....Pages 142-147
Front Matter....Pages 149-149
Universality of the Long Time Tail in Hamiltonian Dynamics....Pages 151-158
Why some H?non-Heiles Potentials are Integrable....Pages 159-165
Chaotic Pulsations in Variable Stars with Harmonic Mode Coupling....Pages 166-170
Front Matter....Pages 149-149
Canonical Forms for Compatible BiHamiltonian Systems....Pages 171-179
Front Matter....Pages 181-181
Transitions from Chaotic to Brownian Motion Behaviour....Pages 183-191
Kinetic Theory for the Standard Map....Pages 192-200
Probabilistic Description of Deterministic Chaos: A Local Equilibrium Approach....Pages 201-203
State Prediction for Chaotic 1-D-Maps....Pages 204-212
Exact and Approximate Reconstruction of Multifractal Coding Measures....Pages 213-217
Conservative Versus Reversible Dynamical Systems....Pages 218-226
A Simple Method to Generate Integrable Symplectic Maps....Pages 227-231
Integrable Mappings and Soliton Lattices....Pages 232-239
Front Matter....Pages 241-241
Integrable Higher Nonlinear Schr?dinger Equations....Pages 243-245
Nonclassical Symmetry Reductions of a Generalized Nonlinear Schr?dinger Equation....Pages 246-254
Direct Methods in Soliton Theories....Pages 255-263
Trilinear Form — An Extension of Hirota’s Bilinear Form....Pages 264-269
On the Use of Bilinear Forms for the Search of Families of Integrable Nonlinear Evolution Equations....Pages 270-274
From Periodic Processes to Solitons and Vice-Versa....Pages 275-280
Front Matter....Pages 281-281
The Crum Transformation for a Third Order Scattering Problem....Pages 283-288
Darboux Theorems Connected to Dym Type Equations....Pages 289-291
Forced Initial Boundary Value Problems for Burgers Equation....Pages 292-297
Creation and Annihilation of Solitons in Nonlinear Integrable Systems....Pages 298-301
Front Matter....Pages 303-303
Multidimensional Nonlinear Schr?dinger Equations Showing Localized Solutions....Pages 305-311
Front Matter....Pages 303-303
New Soliton Solutions for the Davey-Stewartson Equation....Pages 312-320
2 + 1 Dimensional Dromions and Hirota’s Bilinear Method....Pages 321-324
Skyrmions Scattering in (2+1) Dimensions....Pages 325-329
Back Matter....Pages 331-340

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"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Integration of Non-Integrable Systems....Pages 3-24
Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions....Pages 25-36
Soliton Dynamics and Chaos Transition in a Microstructured Lattice Model....Pages 37-45
What is the Role of Dynamical Chaos in Irreversible Processes?....Pages 46-57
A Propositional Lattice for the Logic of Temporal Predictions....Pages 58-70
Damping, Quantum Field Theory and Thermodynamics....Pages 71-75
Quasi-Monomial Transformations and Decoupling of Systems of ODE’s....Pages 76-81
Front Matter....Pages 83-83
Solitons in Optical Fibers: First- and Second-Order Perturbations....Pages 85-98
Similarity Solutions of Equations of Nonlinear Optics....Pages 99-107
Heisenberg Ferromagnet, Generalized Coherent States and Nonlinear Behaviour....Pages 108-110
Integrable Supersymmetric Models and Phase Transitions in One Dimension....Pages 111-114
Denaturation of DNA in a Toda Lattice Model....Pages 115-122
Front Matter....Pages 123-123
A Simple Method to Obtain First Integrals of Dynamical Systems....Pages 125-128
Transition to Turbulence in 1-D Rayleigh-B?nard Convection....Pages 129-134
Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow....Pages 135-137
Spatial Coherent Structures in Dissipative Systems....Pages 138-141
Hierarchies of (1+1)-Dimensional Multispeed Discrete Boltzmann Model Equations....Pages 142-147
Front Matter....Pages 149-149
Universality of the Long Time Tail in Hamiltonian Dynamics....Pages 151-158
Why some H?non-Heiles Potentials are Integrable....Pages 159-165
Chaotic Pulsations in Variable Stars with Harmonic Mode Coupling....Pages 166-170
Front Matter....Pages 149-149
Canonical Forms for Compatible BiHamiltonian Systems....Pages 171-179
Front Matter....Pages 181-181
Transitions from Chaotic to Brownian Motion Behaviour....Pages 183-191
Kinetic Theory for the Standard Map....Pages 192-200
Probabilistic Description of Deterministic Chaos: A Local Equilibrium Approach....Pages 201-203
State Prediction for Chaotic 1-D-Maps....Pages 204-212
Exact and Approximate Reconstruction of Multifractal Coding Measures....Pages 213-217
Conservative Versus Reversible Dynamical Systems....Pages 218-226
A Simple Method to Generate Integrable Symplectic Maps....Pages 227-231
Integrable Mappings and Soliton Lattices....Pages 232-239
Front Matter....Pages 241-241
Integrable Higher Nonlinear Schr?dinger Equations....Pages 243-245
Nonclassical Symmetry Reductions of a Generalized Nonlinear Schr?dinger Equation....Pages 246-254
Direct Methods in Soliton Theories....Pages 255-263
Trilinear Form — An Extension of Hirota’s Bilinear Form....Pages 264-269
On the Use of Bilinear Forms for the Search of Families of Integrable Nonlinear Evolution Equations....Pages 270-274
From Periodic Processes to Solitons and Vice-Versa....Pages 275-280
Front Matter....Pages 281-281
The Crum Transformation for a Third Order Scattering Problem....Pages 283-288
Darboux Theorems Connected to Dym Type Equations....Pages 289-291
Forced Initial Boundary Value Problems for Burgers Equation....Pages 292-297
Creation and Annihilation of Solitons in Nonlinear Integrable Systems....Pages 298-301
Front Matter....Pages 303-303
Multidimensional Nonlinear Schr?dinger Equations Showing Localized Solutions....Pages 305-311
Front Matter....Pages 303-303
New Soliton Solutions for the Davey-Stewartson Equation....Pages 312-320
2 + 1 Dimensional Dromions and Hirota’s Bilinear Method....Pages 321-324
Skyrmions Scattering in (2+1) Dimensions....Pages 325-329
Back Matter....Pages 331-340
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