Waves and structures in nonlinear nondispersive media:General theory and applica（非线性非分散媒介中的波和结构：非线性声学的一般理论及应用）（英文版） mobi 下载 网盘 caj lrf pdf txt 阿里云

本书结合数学模型介绍了非线性非分散介质中的波和结构的基础理论。全书分成两部分：第ⅰ部分给出了很多具体的例子，用于阐明一般的分析方法；第ⅱ部分主要介绍非线性声学的应用，内容包括一些具体的非线性模型及其精确解，非线性的物理机理，锯齿形波的传播，自反应现象，非线性共振及在工程、医学、非破坏性试验、地球物理学等的应用。

本书是硕士生和博士生学习具有各种物理性质的非线性波理论非常实用的教材，也是工程师和研究人员在研究工作中遇到需要考虑和处理非线性波因素时一本很好的参考书。

part i foundati*** of the theory of waves in nondispersive

media

1 nonlinear equati*** of the first order

　1.1 *** wave equation

　　1.1.1 the canonical form of the equation

　　1.1.2 particle flow

　　1.1.3 discussion of the riemann solution

　　1.1.4 compressi*** and expansi*** of the particle flow

　　1.1.5 continuity equation

　　1.1.6 c***truction of the density field

　　1.1.7 momentum-c***ervation law

　　1.1.8 fourier transforms of density and velocity

　1.2 line-growth equation

　　1.2.1 forest-fire propagation

　　1.2.2 anisotropic surface growth

　　1.2.3 solution of the surface-growth equation

　1.3 one-dimensional laws of gravitation

　　1.3.1 lagrangian description of one-dimensional gravitation

　　1.3.2 eulerian description of one-dimensional gravitation

　　1.3.3 collapse of a one-dimensional universe

　1.4 problems to chapter 1

　　references

2 generalized soluti*** of nonlinear equati***

　2.1 standard equati***

　　2.1.1 particle-flow equati***

　　2.1.2 line growth in the small angle approximation

　　2.1.3 nonlinear acoustics equation

　2.2 multistream soluti***

　　2.2.1 interval of single-stream motion

　　2.2.2 appearance of multistreamness

　　2.2.3 gradient catastrophe

　2.3 sum of streams

　　2.3.1 total particle flow

　　2.3.2 summation of streams by inverse fourier transform

　　2.3.3 algebraic sum of the velocity field

　　2.3.4 density of a "warm" particle flow

　2.4 weak soluti*** of nonlinear equati*** of the first order

　　2.4.1 forest fire

　　2.4.2 the lax-oleinik absolute minimum principle

　　2.4.3 geometric c***truction of weak soluti***

　　2.4.4 convex hull

　　2.4.5 maxwell's rule

　2.5 the e-rykov-sinai global principle

　　2.5.1 flow of inelasfically coalescing particles

　　2.5.2 inelastic collisi*** of particles

　　2.5.3 formulation of the global principle

　　2.5.4 mechanical meaning of the global principle

　　2.5.5 condition of physical realizability

　　2.5.6 geometry of the global principle

　　2.5.7 soluti*** of the continuity equation

　2.6 line-growth geometry

　　2.6.1 parametric equati*** of a line

　　2.6.2 contour in polar coordinates

　　2.6.3 contour envelopes

　2.7 problems to chapter 2

　　references

3 nonlinear equati*** of the second order

　3.1 regularization of nonlinear equati***

　　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 equati*** 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

4 field evolution within the framework of the burgers

equation

　4.1 evolution of one-dim***ional signals

　　4.1.1 self-similar solution, once more

　　4.1.2 approach to the linear stage

　　4.1.3 n-wave and u-wave

　　4.1.4 sawtooth waves

　　4.1.5 periodic waves

　4.2 evolution of complex signals

　　4.2.1 quasiperiodic complex signals

　　4.2.2 evolution of fractal signals

　　4.2.3 evolution of multi-scale signals - a dynamic turbulence

model

　4.3 problems to chapter 4

　　references

5 evolution of a noise field within the framework of the burgers

equation

　5.1 burgers turbulence - acoustic turbulence

　5.2 the burgers turbulence at the initial stage of evolution

　　5.2.1 one-point probability density of a random eulerian velocity

field

　　5.2.2 properties of the probability density of a random velocity

field

　　5.2.3 spectra of a velocity field

　5.3 turbulence evolution at the stage of developed

discontinuities

　　5.3.1 phenomenology of the burgers turbulence

　　5.3.2 evolution of the burgers turbulence: statistically

homogeneous potential and velocity (n ] 1 and n [ -3)

　　5.3.3 exact self-similarity (n ] 2)

　　5.3.4 violation of self-similarity (1 [ n [ 2)

　　5.3.5 evolution of turbulence: statistically inhomogeneous

potential (-3 [ n [ 1)

　　5.3.6 statistically homogeneous velocity and inhomogeneous

potential (-1 [ n [ 1)

　　5.3.7 statistically inhomogeneous velocity and in_homogeneous

potential (-3 [ n [ -1)

　　5.3.8 evolution of intense acoustic noise

　　references

6 multidimensional nonlinear equati***

　6.1 nonlinear equati*** of the first order

　　6.1.1 main equati*** of three-dimensional flows

　　6.1.2 lagrangian and eulerian description of a three-dimentional

low

　　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 in***cting particles and a singular

density field

　6.2 multidimensional nonlinear equati*** 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 soluti*** of the multidimensional burgers

equation and local self-similarity

　　6.3.2 evolution of *** localized perturbati***

　　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 perturbati*** with complex internal

structure

　　6.3.6 asymptotic long-time behavior of a localized

perturbation

　　6.3.7 appendix to section 6.3. statistical properties of maxima

of inhomogeneous random gaussian fields

　*** model description of evolution of the large-scale structure of

the universe

　　***.1 gravitational instability in an expanding universe

　　***.2 from the vlasov~poisson equation to the zeldovich

approximation and adhesion model

　　references

　　part ii mathematical models and physical phenomena in nonlinear

acoustics

7 model equati*** and methods of finding their exact

soluti***

　7.1 introduction

　　7.1.1 facts from the linear theory

　　7.1.2 how to add nonlinear terms to simplified equati***

　　7.1.3 more general evolution equati***

　　7.1.4 two types of evolution equati***

　7.2 lie groups and some exact soluti***

　　7.2.1 exact soluti*** of the burgers equation

　　7.2.2 finding exact soluti*** of the burgers equation by using

the group-theory methods

　　7.2.3 some methods of finding exact soluti***

　7.3 the a priori symmetry method

　　references

8 types of acoustic nonlinearities and methods of nonlinear

acoustic diagnostics

　8.1 introduction

　　8.1.1 physical and geometric nonlinearities

　8.2 classification of types of acoustic nonlinearity

　　8.2.1 boundary nonlinearities

　8.3 some mechanisms of bulk structural nonlinearity

　　8.3.1 nonlinearity of media with strongly compressible

inclusi***

　　8.3.2 nonlinearity of solid structurally inhomogeneous

media

　8.4 nonlinear diagnostics

　　8.4.1 inverse problems of nonlinear diagnostics

　　8.4.2 peculiarities of nonlinear diagnostics problems

　8.5 applicati*** of nonlinear diagnostics methods

　　8.5.1 detection of bubbles in a liquid and cracks in a

solid

　　8.5.2 measurements based on the use of radiation pressure

　　8.5.3 nonlinear acoustic diagnostics in c***truction

industry

　8.6 non-typical nonlinear phenomena in structurally inhomogeneous

media

　　references

9 nonlinear sawtooth waves

　9.1 sawtooth waves

　9.2 field and spectral approaches in the theory of nonlinear

waves

　　9.2.1 general remarks

　　9.2.2 generation of harmonics

　　9.2.3 degenerate parametric in***ction

　9.3 diffracting beams of sawtooth waves

　9.4 waves in inhomogeneous media and nonlinear geometric

acoustics

　9.5 the focusing of discontinuous waves

　9.6 nonlinear absorption and saturation

　9.7 kinetics of sawtooth waves

　9.8 in***ction of waves containing shock fronts

　　references

10 self-action of spatially bounded waves containing shock

fronts

　10.1 introduction

　10.2 self-action of sawtooth ultrasonic wave beams due to the

heating of a medium and acoustic wind formation

　10.3 self-refraction of weak shock waves in a quardatically

nonlinear medium

　10.4 non-inertial self-action in a cubically nonlinear

medium

　10.5 symmetries and c***ervation laws for an evolution equation

describing beam propagation in a nonlinear medium

　10.6 conclusi***

　　references

11 nonlinear standing waves, resonance phenomena and frequency

characteristics of distributed systems

　11.1 introduction

　11.2 methods of evaluation of the characteristics of nonlinear

resonators

　11.3 standing waves and the q-factor of a resonator filled with a

dissipating medium

　11.4 frequency resp***es of a quadratically nonlinear

resonator

　11.5 q-factor increase under introduction of losses

　11.6 geometric nonlinearity due to boundary motion

　11.7 resonator filled with a cubically nonlinear medium

　　references

　　appendix fundamental properties of generalized functi***

　a.1 definition of generalized functi***

　a.2 fundamental sequences

　a.3 derivatives of generalized functi***

　a.4 the leibniz formula

　a.5 derivatives of discontinuous functi***

　a.6 generalized functi*** of a composite argument

　a.7 multidimensional generalized functi***

　a.8 continuity equation

　a.8.1 singular solution

　a.8.2 green's function

　a.8.3 lagrangian and eulerian coordinates

　a.9 method of characteristics inde

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书籍介绍

《非线性非分散介质中的波和结构:非线性声学的一般理论及应用(英文版)》结合数学模型介绍了非线性非分散介质中的波和结构的基础理论。全书分成两部分：第ⅰ部分给出了很多具体的例子，用于阐明一般的分析方法；第ⅱ部分主要介绍非线性声学的应用，内容包括一些具体的非线性模型及其精确解，非线性的物理机理，锯齿形波的传播，自反应现象，非线性共振及在工程、医学、非破坏性试验、地球物理学等的应用。

《非线性非分散介质中的波和结构:非线性声学的一般理论及应用(英文版)》是硕士生和博士生学习具有各种物理性质的非线性波理论非常实用的教材，也是工程师和研究人员在研究工作中遇到需要考虑和处理非线性波因素时一本很好的参考书。