Solitons [Paperback]

With contributions by numerous experts1 The Soliton and Its History.- 1.1 Russells Discovery of the Great Solitary Wave.- 1.2 Definition of a Soliton: N-Soliton Solutions of Nonlinear Evolution Equations.- 1.3 B?cklund Transformations and Conserved Densities.- 1.4 Other Physical Problems and the Discovery of the Inverse Method.- 1.5 Operator Pair Formulation of Nonlinear Evolution Equations.- 1.6 Discovery of Some Other N-Soliton Solutions: The AKNS-Zakharov-Shabat 2 ? 2 Scattering Scheme and Its Geometry.- 1.7 Further Progress on Inverse Scattering Methods.- References.- 2. Aspects of Soliton Physics.- 2.1 Historical Remarks and Summary.- 2.2 Model Interacting Systems.- 2.2.1 The Interaction of an Electromagnetic Field with a Two-Level Medium.- 2.2.2 Solitons in Plasma Physics.- 2.3 Inverse Spectral Transformation and Motion Invariants.- 2.3.1 Physical Introduction to the Inverse Scattering Method.- 2.3.2 Physical Information from the Inverse Method.- 2.3.3 Hamiltonian Description and Constants of the Motion.- Appendix A: Formal Derivation of the Marchenko Equations.- References.- 3. The Double SineGordon Equations: A Physically Applicable System of Equations.- 3.1 Physical Background.- 3.2 Theory of Degenerate SIT.- 3.3 Spin Waves in Liquid 3He.- 3.4 Perturbation Theory for the Double Sine-Gordon Equation.- References.- 4. On a Nonlinear Lattice (The Toda Lattice).- 4.1 Nonlinear Lattices.- 4.1.1 Equations of Motion.- 4.1.2 The Dual Transformation.- 4.2 The Exponential Interaction.- 4.2.1 Cnoidal Waves.- 4.2.2 Solitons.- 4.2.3 The Harmonic Limit.- 4.2.4 Two-Soliton Solutions.- 4.3 Matrix Formalism.- 4.3.1 The Inverse Method.- 4.3.2 Multi-Soliton Solutions.- 4.4 The Continuum Limit.- 4.5 B?cklund Transformations.- 4.6 Concluding Remarks.- References.- 5. Direct Methods in Soliton Theory.- 5.1 Preliminaries.- 5.2 Properties of the D Operator.- 5.3 Solutions of the Bilinear Differential Equations.- 5.4 N-Soliton Solution of KdV-Type Equations.- 5.5 B?cklund Translã