Physics of Gravitating Systems II: Nonlinear Collective Processes: Nonlinear Waves, Solitons, Collisionless Shocks, Turbulence. Astrophysical Applications

(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- VII Problems of Nonlinear Theory.- II Astrophysical Applications.- VIII General Remarks.- IX Spherical Systems.- X Ellipsoidal Systems.- XI Disk-like Systems. Spiral Structure.- XII Other Applications.- § 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- § 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- § 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- § 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- § 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. “Lagrange” Derivation of the Matrix Equation.- § 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- § 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- § 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- § 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- § 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- §11. Derivation of the Kinetic Equation for Waves.- § 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.