非线性波数学物理学入门 哈尔滨工业大学出版社 pdf 夸克云 tct umd 下载 2025 azw3 kindle

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 functi***

1.4.1 Definiti***

1.4.2 Differentiation

1.4.3 Reverse functi*** 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 Solit*** and adiabatic potentials

3.t The Korteweg-deVries equation

3.2 Steady soluti*** of the Korteweg-deVries equation

3.3 Developing equati*** of nonlinear vecto***aves

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 ***ysis

Exercises

4 Structural phase transiti***

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 Nonlinea***aves

5.1 Elemental waves

5.2 Matrix formulation for nonlinear development

5.3 Heat dissipation of wave motion

5.4 Born-Huang transiti*** 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 functi*** for coherent wave packets

7.1.2 Fourier transforms and Marchenko's equati***

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 ***tationary 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 equati***

9.1 The Klein-Gordon equation

9.2 The Backlund transformation

9.3 The sine-Gordon equation

9.4 Numerical ***ysis of the sine-Gordon equation

9.5 Inverse scatterings and the Backlund transformation

9.6 Scatterings by a pseudopotential

10 Miscellaneous applicati***

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 transiti*** by pseudopotentials

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