3 Nonlinear Equations of the Second Order

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

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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
- 3.1 Regularization of nonlinear equations
- 3.1.1 The Kardar-Parisi-Zhang equation
- 3.1.2 The Burgers equation
- 3.2 Properties of the Burgers equation
- 3.2.1 Galilean invariance
- 3.2.2 Reynolds number
- 3.2.3 Hubble expansion
- 3.2.4 Stationary wave
- 3.2.5 Khokhlov’s solution
- 3.2.6 Rudenko’s solution
- 3.3 General solution of the Burgers equation
- 3.3.1 The Hopf-Cole substitution
- 3.3.2 General solution of the Burgers equation
- 3.3.3 Averaged Lagrangian coordinate
- 3.3.4 Solution of the Burgers equation with vanishing viscosity
- 3.4 Model equations of gas dynamics
- 3.4.1 One-dimensional model of a polytropic gas
- 3.4.2 Discussion of physical properties of a model gas
- 3.5 Problems to Chapter 3
- References

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