醉染图书非线波数学物理学入门9787560396163

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 Jacobis 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 lent
2.1.1 Phase of propagation

2.1.2 Energy flow

2.1.3 Scattering by an oscillator

2.2 Microwave transmission

. Schr6dingers 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 Bargmanns theorem

3.4.1 One-soliton solution

3.4.2 Two-soliton solution

3.5 Riccatis theorem

3.6 Properties of the Eckart potential in the soliton field

3.7 Zabusky-Kruskals computational analysis

Exercises

4 Structural phase transitions

4.1 Initial uncertainties and transition anomalies

4.1.1 Specific heat anomalies

4.1.2 Landaus 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 description

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.. 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 Marchenkos equation

7.1.1 Delta and truncated step functions for coherent wave packets

7.1.2 Fourier transforms and Marchenkos 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 si-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 throu asorbing 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 Tos ttce

10.5.2 Aperiodic transitions by pseudopotentials

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