非线性波数学物理学入门 (加)藤本实 著 txt umd azw3 下载 fb2 pdf 在线 免费

本书是为高年级本科生和研究生编写的，是一本关于非线性物理学的升级物理课程的教科书。尽管如此，非线性数学仍以双曲函数和椭圆函数为。本书共十章，用非齐次微分方程来分析非线性问题获得的相关信息，主要内容包括：经典力学中的非线性特征、波传播、奇异性与边界、孤立子与热势、结构相变、非线性波、散射理论、逆散射法、准静态孤子态、贝可隆变换与正弦-戈登方程等。本书还回顾了物理实践中的代表性案例，然后通过一般理论进行了应用。

1 Nonlinearity in classical mechanics

1.1 A pendulum

1.1.1 Oscillation

1.1.2 Vertical rotation

1.2 Vibration by a nonlinear spring force

1.3 A jumping rope

1.4 Hyperbolic and elliptic functions

1.4.1 Definitions

1.4.2 Differentiation

1.4.3 Reverse functions cn-1 and dn-1

1.4.4 Periodicity of Jacobi's sn-function

1.5 Variation principle

1.6 Buckling deformation of a rod

Exercise

2 Wave propagation,singularities and boundaries

2.1 Elastic waves along a linear string of infinite length

2.1.1 Phase of propagation

2.1.2 Energy flow

2.1.3 Scattering by an oscillator

2.2 Microwave transmission

2.3 Schr6dinger's equation

2.4 Scattering by the potential V(x)=Vo sech2 x

2.5 Two-dimensional waves in inhomogeneous medium

2.6 Sound propagation in air

Exercises

3 Solitons and adiabatic potentials

3.t The Korteweg-deVries equation

3.2 Steady solutions of the Korteweg-deVries equation

3.3 Developing equations of nonlinear vector waves

3.4 Bargmann's theorem

3.4.1 One-soliton solution

3.4.2 Two-soliton solution

3.5 Riccati's theorem

3.6 Properties of the Eckart potential in the soliton field

3.7 Zabusky-Kruskal's computational analysis

Exercises

4 Structural phase transitions

4.1 Initial uncertainties and transition anomalies

4.1.1 Specific heat anomalies

4.1.2 Landau's theory

4.2 Dynamical theory of collective motion

4.2.1 Longitudinal waves

4.2.2 Transverse waves

4.3 Pseudopotential and sine-Gordon equation

Exercises

5 Nonlinear waves

5.1 Elemental waves

5.2 Matrix formulation for nonlinear development

5.3 Heat dissipation of wave motion

5.4 Born-Huang transitions in crystals

5.5 Symmetry of media for the Korteweg-deVries equation

5.6 Soliton deion

Exercise

6 Scattering theory

6.1 One-component waves

6.1.1 Scatterings of elemental waves

6.1.2 Singularity of a soliton potential

6.2 Two-component scatterings

6.2.1 A two-component wave

6.2.2 Reflection and transmission

6.2.3 Poles of transmission and reflection coefficients

6.2.4 Soliton potentials

6.2.5 Asymptotic expansion

Exercises

7 Method of inverse scatterings

7.1 Coherent wave packets and Marchenko's equation

7.1.1 Delta and truncated step functions for coherent wave packets

7.1.2 Fourier transforms and Marchenko's equations

7.2 Reflectionless multi-soliton potentials

7.3 Two-component systems

7.3.1 Inverse scatterings

7.3.2 Matrix method

7.3.3 Modified Korteweg-deVries equation,part 1

Exercises

8 Quasi-static soliton states

8.1 Developing the Korteweg-deVries equation

8.1.1 N onstationary states

8.1.2 Thermal perturbation

8.2 Multi-soliton potentials in unsteady states

8.3 The modified Korteweg-deVries equation,part 2

8.4 Thermodynamic instability and Breezer potentials

8.5 The third-order Schrodinger equation

Exercises

9 The Baicklund transformation and sine-Gordon equations

9.1 The Klein-Gordon equation

9.2 The Backlund transformation

9.3 The sine-Gordon equation

9.4 Numerical analysis of the sine-Gordon equation

9.5 Inverse scatterings and the Backlund transformation

9.6 Scatterings by a pseudopotential

10 Miscellaneous applications

10.1 Surface waves

10.1.1 The first approximation

10.1.2 The second approximation

10.2 Vortex motion in fluid media

10.2.1 A vortex

10.2.2 Vortex motion

10.3 Plasma oscillation

10.4 Laser light transmission through absorbing media

10.4.1 Two-level atom in an intense radiation field

10.4.2 Scattering of intense radiation

10.4.3 Sine-Gordon limit

10.5 Periodic lattices

10.5.1 Toda's lattice

10.5.2 Aperiodic transitions by pseudopotentials

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