Solitons and Chaos

Softcover Nachdruck of the original 1. Auflage 1991
ISBN: 978-3-540-54389-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 336 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 546 g

Reihe: Research Reports in Physics

Solitons and Chaos presents some recent contributions to our understanding of these two complementary aspects of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. Both specialists and graduate students will find this update on the state of the art useful.

Zielgruppe

Research

Autoren/Hrsg.

Lambert, Franklin J.

Antoniou, Ioannis

Inhaltsverzeichnis

I General Questions on Chaos and Integrability.- Integration of Non-Integrable Systems.- Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions.- Soliton Dynamics and Chaos Transition in a Microstructured Lattice Model.- What is the Role of Dynamical Chaos in Irreversible Processes?.- A Propositional Lattice for the Logic of Temporal Predictions.- Damping, Quantum Field Theory and Thermodynamics.- Quasi-Monomial Transformations and Decoupling of Systems of ODE’s.- II Physical Systems with Soliton Ingredients.- Solitons in Optical Fibers: First- and Second-Order Perturbations.- Similarity Solutions of Equations of Nonlinear Optics.- Heisenberg Ferromagnet, Generalized Coherent States and Nonlinear Behaviour.- Integrable Supersymmetric Models and Phase Transitions in One Dimension.- Denaturation of DNA in a Toda Lattice Model.- III Dissipative Systems.- A Simple Method to Obtain First Integrals of Dynamical Systems.- Transition to Turbulence in 1-D Rayleigh-Bénard Convection.- Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow.- Spatial Coherent Structures in Dissipative Systems.- Hierarchies of (1+1)-Dimensional Multispeed Discrete Boltzmann Model Equations.- IV Hamiltonian Systems.- Universality of the Long Time Tail in Hamiltonian Dynamics.- Why some Hénon-Heiles Potentials are Integrable.- Chaotic Pulsations in Variable Stars with Harmonic Mode Coupling.- Canonical Forms for Compatible BiHamiltonian Systems.- V Maps and Cascades.- Transitions from Chaotic to Brownian Motion Behaviour.- Kinetic Theory for the Standard Map.- Probabilistic Description of Deterministic Chaos: A Local Equilibrium Approach.- State Prediction for Chaotic 1-D-Maps.- Exact and Approximate Reconstruction of Multifractal CodingMeasures.- Conservative Versus Reversible Dynamical Systems.- A Simple Method to Generate Integrable Symplectic Maps.- Integrable Mappings and Soliton Lattices.- VI Direct Methods Applicable to Soliton Systems.- Integrable Higher Nonlinear Schrödinger Equations.- Nonclassical Symmetry Reductions of a Generalized Nonlinear Schrödinger Equation.- Direct Methods in Soliton Theories.- Trilinear Form — an Extension of Hirota’s Bilinear Form.- On the Use of Bilinear Forms for the Search of Families of Integrable Nonlinear Evolution Equations.- From Periodic Processes to Solitons and Vice-Versa.- VII Inverse Methods Related to a Linearization Scheme.- The Crum Transformation for a Third Order Scattering Problem.- Darboux Theorems Connected to Dym Type Equations.- Forced Initial Boundary Value Problems for Burgers Equation.- Creation and Annihilation of Solitons in Nonlinear Integrable Systems.- VIII Nonlinear Excitations in more than one Space Dimension.- Multidimensional Nonlinear Schrödinger Equations Showing Localized Solutions.- New Soliton Solutions for the Davey-Stewartson Equation.- 2+1 Dimensional Dromions and Hirota’s Bilinear Method.- Skyrmions Scattering in (2+1) Dimensions.- Index of Contributors.