6 Multidimensional Nonlinear Equations

Waves and structures in nonlinear nondis 作者：S.N. Gurbatov, O.V. Rudenko,　　 ISBN：978-7-04-031695-7　出版时间：2011-08-30

内封

版权

目录

Front Matter

Part I Foundations of the Theory of Waves in Nondispersive Media

1 Nonlinear Equations of the First Order

2 Generalized Solutions of Nonlinear Equations

3 Nonlinear Equations of the Second Order

4 Field EvolutionWithin the Framework of the Burgers Equation

5 Evolution of a Noise Field Within the Framework of the Burgers Equation

6 Multidimensional Nonlinear Equations

Part II Mathematical Models and Physical Phenomena in Nonlinear Acoustics

7 Model Equations and Methods of Finding Their Exact Solutions

8 Types of Acoustic Nonlinearities and Methods of Nonlinear Acoustic Diagnostics

9 Nonlinear Sawtooth Waves

10 Self-action of Spatially BoundedWaves Containing Shock Fronts

11 Nonlinear Standing Waves, Resonance Phenomena and Frequency Characteristics of Distributed Systems

Appendix Fundamental Properties of Generalized Functions

Index
- 6.1 Nonlinear equations of the first order
- 6.1.1 Main equations of three-dimensional flows
- 6.1.2 Lagrangian and Eulerian description of a three-dimentional flow
- 6.1.3 Jacobian matrix for the transformation from Lagrangian to Eulerian coordinates
- 6.1.4 Density of a multidimensional flow
- 6.1.5 Weak solution of the surface-growth equation
- 6.1.6 Flows of locally interacting particles and a singular density field
- 6.2 Multidimensional nonlinear equations of the second order
- 6.2.1 The two-dimensional KPZ equation
- 6.2.2 The three-dimensional Burgers equation
- 6.2.3 Model density field
- 6.2.4 Concentration field
- 6.3 Evolution of the main perturbation types in the KPZ equation and in the multidimensional Burgers equation
- 6.3.1 Asymptotic solutions of the multidimensional Burgers
- equation and local self-similarity
- 6.3.2 Evolution of simple localized perturbations
- 6.3.3 Evolution of periodic structures under infinite Reynolds numbers
- 6.3.4 Evolution of the anisotropic Burgers turbulence
- 6.3.5 Evolution of perturbations with complex internal structure
- 6.3.6 Asymptotic long-time behavior of a localized perturbation
- 6.3.7 Appendix to Section 6.3Statistical properties of maxima of inhomogeneous random Gaussian fields
- 6.4 Model description of evolution of the large-scale structure of the Universe
- 6.4.1 Gravitational instability in an expanding Universe
- 6.4.2 From the Vlasov-Poisson equation to the Zeldovich approximation and adhesion model
- References

Book Metrics 引用导出

点击：次

下载：次