Soliton Phenomenology [Paperback]

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 ?5Schr?dinger 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 Schr?dinger 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 Schr?dinger 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, inl3¡