A good deal of the material presented in this book has been prepared by top experts in the field lecturing in January 1987 at the Winter School on Solitons in Tiruchirapalli,India. The lectures begin at an elementary level but go on to include even the most recent developments in the field. The book makes a handy introduction to the various facets of the soliton concept, and will be useful both to newcomers to the field and to researchers who are interested in developments in new branches of physics and mathematics.
A good deal of the material presented in this book has been prepared by top experts in the field lecturing in January 1987 at the Winter School on Solitons in Tiruchirapalli,India. The lectures begin at an elementary level but go on to include even the most recent developments in the field. The book makes a handy introduction to the various facets of the soliton concept, and will be useful both to newcomers to the field and to researchers who are interested in developments in new branches of physics and mathematics.
I Introduction.- Inaugural Address - The Dynamics of Dynamics.- "The Wave" "Par Excellence", the Solitary Progressive Great Wave of Equilibrium of the Fluid: An Early History of the Solitary Wave (With 8 Figures).- II Mathematical Theory: IST, Symmetries, Singularity Structure and Integrability.- Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions.- Inverse Problems and a Unified Approach to Integrability in 1, 1+1 and 2+1 Dimensions.- Gauge Unification of Integrable Nonlinear Systems (With 3 Figures).- Prolongation Structure in One and Two Dimensions.- Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems.- Painlevé Analysis and Integrability Aspects of Nonlinear Evolution Equations.- Generalised Burgers Equations and Connection Problems for Euler-Painlevé Transcendents.- Bäcklund Transformations and Soliton Wave Functions.- Comparison of Some Numerical Schemes for the K-dV Equation.- K-dV Like Equations with Domain Wall Solutions and Their Hamiltonians.- III Lattice Solitons.- Lattice Solitons and Nonlinear Diatomic Models.- Recent Results in Toda Lattice.- Construction of Exact Invariants for One- and Two-Dimensional Classical Systems.- Nonlinear Chains and Kink-Impurity Interactions.- IV Statistical Mechanics and Quantum Aspects.- Quantum Solitons: An Overview.- Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models.- Exactly Solvable Models in Statistical Mechanics (With 12 Figures).- V Applications: Physics and Biology.- Solitons and Some Other Special Solutions in Field Theory.- Solitary Waves of the "2-Dimensional Ferromagnet".- Soliton Propagation in Optical Fibres (With 2 Figures).- Davydov's Soliton.- Generalized NonlinearSchrödinger Equations in Quantum Fluid Dynamics.- Index of Contributors.
I Introduction.- Inaugural Address - The Dynamics of Dynamics.- "The Wave" "Par Excellence", the Solitary Progressive Great Wave of Equilibrium of the Fluid: An Early History of the Solitary Wave (With 8 Figures).- II Mathematical Theory: IST, Symmetries, Singularity Structure and Integrability.- Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions.- Inverse Problems and a Unified Approach to Integrability in 1, 1+1 and 2+1 Dimensions.- Gauge Unification of Integrable Nonlinear Systems (With 3 Figures).- Prolongation Structure in One and Two Dimensions.- Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems.- Painlevé Analysis and Integrability Aspects of Nonlinear Evolution Equations.- Generalised Burgers Equations and Connection Problems for Euler-Painlevé Transcendents.- Bäcklund Transformations and Soliton Wave Functions.- Comparison of Some Numerical Schemes for the K-dV Equation.- K-dV Like Equations with Domain Wall Solutions and Their Hamiltonians.- III Lattice Solitons.- Lattice Solitons and Nonlinear Diatomic Models.- Recent Results in Toda Lattice.- Construction of Exact Invariants for One- and Two-Dimensional Classical Systems.- Nonlinear Chains and Kink-Impurity Interactions.- IV Statistical Mechanics and Quantum Aspects.- Quantum Solitons: An Overview.- Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models.- Exactly Solvable Models in Statistical Mechanics (With 12 Figures).- V Applications: Physics and Biology.- Solitons and Some Other Special Solutions in Field Theory.- Solitary Waves of the "2-Dimensional Ferromagnet".- Soliton Propagation in Optical Fibres (With 2 Figures).- Davydov's Soliton.- Generalized NonlinearSchrödinger Equations in Quantum Fluid Dynamics.- Index of Contributors.
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