Soliton Phenomenology

References.- I. Quantum Systems and Classical Behaviour.- 1. Some physical models and nonlinear differential equations.- 1. Magnetic chain (the Heisenberg model).- 2. Magnetic chain with magnon-phonon interaction.- 3. Nonlinearity of exchange integrals andphonon anharmonism in the Heisenberg model.- 4. Anisotropic magnetic chain in an external field breaking U(1)(XY) symmetry.- 5. Generalized Hubbard model.- 6. Low frequency wave interaction with a packet of h.f. waves in plasmas.- 7. The ?5Schrodinger equation as a model to describe collective motions in nuclei.- 8. 'Colour' generalization of a magnetic chain with magnon-phonon interaction.- 9. Multicolour Hubbard model.- 2. Physically interesting nonlinear differential equations.- 1. Equations with quadratic dispersion.- 2. Equations with 'linear' dispersion.- 3. Relativistically-invariant equations.- 4. Dynamical systems given by differential-difference equations.- References.- II. Some Exact Results in One-Dimensional Space.- 3. The Nonlinear Schrodinger equation and the Landau-Lifshitz equation.- 1. NSE associated with a symmetric space.- 2. The Sigma model representation of the NSE and the isotropic Landau-Lifshitz equation.- 3. Gauge connections of the LLE with uniaxial anisotropy and the NSE.- 4. Nonlinear Schrodinger equation with U(p,q) internal symmetry and the SG equation.- 1. Equations of motion and the internal symmetry group.- 2. U(p,q) NSE under trivial boundary conditions.- 3. The U(1,0) model.- 4. The U(0,1) model.- 5. The U(1,1) model.- 6. Quasi-classical quantization of the U(1,1) NSE.- 7. The SG equation.- References.- III. Noncompact Symmetries and Bose Gas.- 5. Dynamical symmetry and generalized coherent states.- 1. Bose gas and dynamical symmetry group.- 2. Quantum version (GCS).- 3. Quantum version. The representation in the form of a path integral over GCS.- 4. Quantum version. Some concrete models with dynamical symmetry.- 5. Weakly nonideal Bose gas. A classical approach.- 6. Bose gas, integrable NSE and Landau-Lifshitz models.- 1. Quantum models and nonlinear classical models corresponding to them. A new formulation of the reduction procedure.- 2. Nonlinear one-dimensional integrable models.- 3. The isotropic Landau-Lifshitz SU(1,1) model.- 4. Bose gas models and nonlinear sigma models. Summary.- 5. The third version - The sigma-model representation connected with the nonlinear Schrodinger equation.- 6. On the reduction procedure.- 7. ?6theory and Bose-drops.- 1. General relations and solitons - drops (particle-like solutions).- 2. Condensate states and their weak excitations.- 3. Localized soliton-like excitations of the condensate.- References.- IV. Soliton-Like Solutions in One-Dimension.- 8. The class of soliton solutions to the vector version of NSE with self-consistent potentials.- 1. Soliton solutions to the U(n) NSE. Linearization method.- 2. U(2) NSE. Dubrovin-Krichever technique.- 3. The self-consistent conditions.- 4. U(2) NSE. A modification of the Dubrovin-Krichever technique.- 5. U(n) system with the Boussinesq potential.- 9. The existence of soliton-like solutions.- 1. Virial relations.- 2. Mechanical analogy method.- 10. Soliton stability.- 1. Stability of hole-like excitations in the ?6model of nonlinear Schrodinger equation. The spectral analysis.- 2. Stability of drop-like solitons. Variational methods.- 3. Structural stability.- References.- V. Phenomenology of D = 1 Solitons.- 11. Dynamics of the formation and interaction of plane solitons.- 1. Computational procedures.- 2. KdV-like equations.- 3. NSE-like equations.- 4. Equation for induced processes.- 5. Relativistically invariant equations (RIE).- 6. Bound states of solitons (bions).- 7. Kink-antikink interactions in the ?4model.- 8. Kink-antikink collisions in the MSG model.- 9. Bions in the ?4-theory.- 10. Small-amplitude expansions.- 12. Structural stability and pinning of solitons.- 1. Static bound states.- 2. Bifurcational perturbation theory.- 3. Static states of the long Josephson junction with a single inhomogeneity.- 4. Passing region.- 13. Dynamical structure factors of soliton gas.- 1. General technique to calculate the dynamical formfactors of solitons.- 2. Dynamic structure factor scattering on a soliton gas. The SG model: phenomenological approach.- 3. CsNiF3and the SG model.- 4. The ideal gas phenomenology and the ?4-model.- 5. Soliton gas kinetics.- 6. Turbulence of a soliton gas.- References.- VI. Many-Dimensional Solitons.- 14. Existence and stability.- 1. Existence.- 2. Quasi-stationary solitons.- 3. Stability of many-dimensional stationary solitons.- 4. Static ring-shaped fluxons (the structure stability).- 15. Pulsons and Q-solitons.- 1. Collapse of circular and spherical bubbles.- 2. Properties of pulsons.- 3. Pulson stability.- 4. Pulson interaction.- 16. Interaction of Q-solitons.- 1. Nonrelativistic models.- 2. Relativistic models.- 3. Formfactors and DSF.- References.