1．Generalized Boltzmann Equation 1
1.1. Mathematical Introduction-Method of Many Scales 1
1.2. Hierarchy of Bogolubov Kinetic Equations 11
1.3. Derivation of the Generalized Boltzmann Equation 15
1.4. Generalized Boltzmann H-Theorem and the Problem of Irreversibility of Time 31
1.5. Generalized Boltzmann Equation and Iterative Construction of Higher-Order Equations in the Boltzmann Kinetic Theory 43
1.6. Generalized Boltzmann Equation and the Theory of Non-Local Kinetic Equations with Time Delay 46
2．Theory of Generalized Hydrodynamic Equations 53
2.1. Transport of Molecular Characteristics 53
2.2. Hydrodynamic Enskog Equations 55
2.3. Transformations of the Generalized Boltzmann Equation 56
2.4. Generalized Continuity Equation 58
2.5. Generalized Momentum Equation for Component 60
2.6. Generalized Energy Equation for Component 63
2.7. Summary of the Generalized Enskog Equations and Derivation of the 67
Generalized Hydrodynamic Euler Equations 67
3．Quantum Non-Local Hydrodynamics 77
3.1. Generalized Hydrodynamic Equations and Quantum Mechanics 77
3.2. GHEs，Quantum Hydrodynamics.SE as the Consequence of GHE 82
3.3. SE and its Derivation from Liouville Equation 88
3.4. Direct Experimental Confirmations of the Non-Local Effects 89
4．Application of Unified Non-Local Theory to the Calculation of the Electron and Proton lnner Structures 97
4.1. Generalized Quantum Hydrodynamic Equations 97
4.2. The Charge Internal Structure of Electron 100
4.3. The Derivation of the Angle Relaxation Equation 106
4.4. The Mathematical Modeling of the Charge Distribution in Electron and Proton 108
4.5. To the Theory of Proton and Electron as Ball-like Charged Objects 129
5．Non-Local Quantum Hydrodynamics in the Theory of Plasmoids and the Atom Structure 131
5.1. The Stationary Single Spherical Plasmoid 131
5.2. Results of the Mathematical Modeling of the Rest Solitons 133
5.3. Nonstationarv 1D Generalized Hydrodynamic Equations in the Self-Consistent Electrical Field.Quantization in the Generalized Quantum Hydrodynamics 141
5.4. Moving Quantum Solitons in Self-Consistent Electric Field 144
5.5. Mathematical Modeling of Moving Solitons 146
5.6. Some Remarks Concerning CPT(harge-Parity-Time)Principle 156
5.7. About Some Mysterious Events of the Last Hundred Years 162
5.7.1. Tunguska Event(TE) 162
5.7.2. Gagarin and Seryogin Air Crash 164
5.7.3. Accident with Malaysia Airlines Flight MH370 166
6．Quantum Solitons in Solid Matter 169
6.1. Quantum Oscillators in the Unified Non-Local Theory 169
6.2. Application of Non-Local Quantum Hydrodynamics to the Description of the Charged Density Waves in the Graphene Crystal Lattice 177
6.3. Generalized Quantum Hydrodynamic Equations Describing the Soliton Movement in the Crystal Lattice 179
6.4. Results of the Mathematical Modeling Without the External Electric Field 189
6.5. Results of the Mathematical Modeling With the External Electric Field 213
6.6. Spin Effects in the Generalized Quantum Hydrodynamic Equations 232
6.7. To the Theory of the SC 239
7．Generalized Boltzmann Physical Kinetics in Physics of Plasma 243
7.1. Extension of Generalized Boltzmann Physical Kinetics for the Transport Processes Description in Plasma 243
7.2. Dispersion Equations of Plasma in Generalized Boltzmann Theory 250
7.3. The Generalized Theory of Landau Damping 254
7.4. Evaluation of Landau Integral 256
7.5. Estimation of the Accuracy of Landau Approximation 264
7.6. Alternative Analytical Solutions of the Vlasov-Landau Dispersion Equation 268
7.7. The Generalized Theory of Landau Damping in Collisional Media 275
8．Physics of a Weakly Ionized Gas 285
8.1. Charged Particles Relaxation in"Maxwellian"Gas and the Hydrodynamic Aspects of the Theory 285
8.2. Distribution Function(DF)of the Charged Particles in the"Lorentz"Gas 288
8.3. Charged Particles in Alternating Electric Field 299
8.4. Conductivity of a Weakly Ionized Gas in the Ctossed Electric and Magnetic Fields 301
8.5. Investigation of the GBE for Electron Energy Distribution in a Constant Electric Field with due Regard for Inelastic Collisions 306
9．Generalized Boltzmann Equation in the Theory of the Rarefied Gases and Liquids 315
9.1. Kinetic Coefficients in the Theory of the Generalized Kinetic Equations.Linearization of the Generalized Boltzmann Equation 315
9.2. Approximate Modified Chapman-Enskog Method 321
9.3. Kinetic Coefficient Calculation with Taking into Account the Statistical Fluctuations 329
9.4. Sound Propagation Studied with the Generalized Equations of Fluid Dynamics 333
9.5. Shock Wave Structure Examined with the Generalized Equations of Fluid Dynamics 345
9.6. Boundary Conditions in the Theory of the Generalized Hydrodynamic Equations 347
9.7. To the Kinetic and Hydrodynamic Theory of Liquids 352
10．Strict Theory of Turbulence and Some Applications of the Generalized Hydrodynamic Theory 363
10.1. About Principles of Classical Theory of Turbulent Flows 363
10.2. Theory of Turbulence and Generalized Euler Equations 364
10.3. Theory of Turbulence and the Generalized Enskog Equations 373
10.4. Unsteady Flow of a Compressible Gas in a Cavity 377
10.5. Application of the GHE：To the Investigation of Gas Flows in Channels with a Step 387
10.6. Vortex and Turbulent Flow of Viscous Gas in Channel with Flat Plate 395
11．Astrophysical Applications 413
11.1. Solution of the Dark Matter Problem in the Frame of the Non-Local Physics 413
11.2. Plasma-Gravitational Analogy in the Generalized Theory of Landau Damping 414
11.3. Disk Galaxy Rotation and the Problem of Dark Matter 425
11.4. Hubble Expansion and the Problem of Dark Energy 438
11.5. Propagation of Plane Gravitational Waves in Vacuum with Cosmic Microwave Background 445
11.6. Application of the Non-Local Physics in the Theory of the Matter Movement in Black Hole 461
11.7. Self-similar Solutions of the Non-Local Equations 469
11.7.1. Preliminary Remarks 469
11.7.2. Self-similar Solutions of the Non-Local Equations in the Astrophysical Appl ications 472
12．The Generalized Relativistic Kinetic Hydrodynamic Theory 493
12.1. Hydrodynamic Form of the Dirac Quantum Relativistic Equation 493
12.2. Generalized Relativistic Kinetic Equation 497
12.3. Generalized Enskog Relativistic Hydrodynamic Equations 502
12.3.1. Derivation of the Continuity Equation 502
12.3.2. Derivation of the Motion Equation 504
12.3.3. Derivation of the Energy Equation 506
12.4. Generalized System of the Relativistic Hydrodynamics and Transfer to the Generalized Relativistic Non-Local Euler Hydrodynamic Equations 508
12.5. Generalized Non-Local Relativistic Euler Equations 513
12.6. The Limit Transfer to the Non-Relativistic Generalized Non-Local Euler Equations 516
12.6.1. Some Auxiliary Expressions 516
12.6.2. Non-Relativistic Generalized Eu ler Equations as Asymptotic of the Relativistic Equations 517
12.7. Expansion of the Flat Harmonic Waves of Small Amplitudes in Ultra-Relativistic Media 520
Some Remarks to the Conclusion of the Monograph 531
Appendix 1．Perturbation Method of the Equation Solution Related to T[f] 533
Appendix 2．Using of Curvilinear Coordinates in the Generalized Hydrodynamic Theory 537
Appendix 3．Characteristic Scales in Plasma Physics 557
Appendix 4．Dispersion Relations in the Generalized Boltzmann Kinetic Theory Neglecting the Integral Collision Term 559
Appendix 5．Three-Diagonal Method of Gauss Elimination Techniques for the Differential Third-and Second-Order Equations 561
Appendix 6．Some Integral Calculations in the Generalized Navier-Stokes Approximation 567
Appendix 7．Derivation of Energy Equation for Invariant Eα=mαV2α/2+εα 569
Appendix 8．To the Non-Local Theory of Cold Nuclear Fusion 575
Appendix 9．To the Non-Local Theory of Variable Stars 583
Appendix 10．To the Non-Local Theory of Levitation 593
References 601
Index 609