Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1. The Hydrodynamic-type Equations and the Solitary Solutions -- 1.1. Introduction -- 1.2. The Korteweg-de Vries equation and the soliton solutions -- 1.3. The Korteweg-de Vries equation with a small perturbation -- 1.4. The linear WKB technique and its generalization -- 1.5. Acknowledgments -- 1.6. References -- Chapter 2. The Nonlinear WKB Technique and Asymptotic Soliton-like Solutions to the Korteweg-de Vries Equation with Variable Coefficients and Singular Perturbation -- 2.1. Introduction

2.2. Main notations and definitions -- 2.3. The structure of the asymptotic one-phase soliton-like solution -- 2.4. The KdV equation with quadratic singularity -- 2.5. Equations for the regular part of the asymptotics and their analysis -- 2.6. Equations for the singular part of the asymptotics and their analysis -- 2.6.1. The main term of the singular part -- 2.6.2. The higher terms of the singular part and the orthogonality condition -- 2.6.3. The orthogonality condition and the discontinuity curve -- 2.6.4. Prolongation of the singular terms from the discontinuity curve

2.7. Justification of the algorithm -- 2.8. Discussion and conclusion -- 2.9. Acknowledgments -- 2.10. References -- Chapter 3. Asymptotic Analysis of the vcKdV Equation with Weak Singularity -- 3.1. Introduction -- 3.2. The asymptotic soliton-like solutions -- 3.3. The examples of the asymptotic soliton-like solutions -- 3.3.1. The asymptotic step-wise solutions -- 3.3.2. The asymptotic solutions of soliton type -- 3.4. Discussion and conclusion -- 3.5. Acknowledgments -- 3.6. References -- Chapter 4. Modeling of Heterogeneous Fluid Dynamics with Phase Transitions and Porous Media

4.1. Introduction -- 4.2. The large particle method -- 4.3. The particle-in-cell method -- 4.4. Modeling of heterogeneous fluid dynamics -- 4.5. Modeling of heterogeneous fluid dynamics with phase transitions -- 4.6. Modeling of viscous fluid dynamics and porous media -- 4.7. References -- Chapter 5. Mathematical Models and Control of Functionally Stable Technological Process -- 5.1. Introduction -- 5.2. Analysis of production process planning procedure -- 5.3. Mathematical model of the production process management system of an industrial enterprise -- 5.4. Control design

5.5. Algorithm of control of production process -- 5.6. Conclusion -- 5.7. Acknowledgments -- 5.8. References -- Chapter 6. Alternative Direction Multiblock Method with Nesterov Acceleration and Its Applications -- 6.1. Introduction -- 6.2. Proximal operators -- 6.3. ADMM (alternating direction method of multipliers) -- 6.4. Bregman iteration -- 6.5. Forward-backward envelope (FBE) -- 6.6. Douglas-Rachford envelope (DRE) -- 6.7. Proximal algorithms for complex functions -- 6.8. Fast alternative directions methods -- 6.9. Numerical experiments -- 6.9.1. Exchange problem