Unidirectional Wave Motions, Volume 23

Preface

Introduction

Part I

1. Flexible string movements

2. Discontinuous solutions of the wave equation

3. String profiles with a moving vertex

4. Periodic wave functions

5. Variable wave patterns

6. Causality and the superposition of exponential wave functions

7. Conditions for permanence and exponential decay of progressive wave profiles

8. Movements of a heavy chain and a compressible medium

9. A third order (viscoelastic) equation of motion

10. Influence of viscoelasticity on signal transmission

11. String vibrations and the Doppler effect

12. Excitation of a string by a fixed or moving local force

13. Boundary conditions and normal modes of vibration

14. Solution of an inhomogeneous wave equation on a finite coordinate interval

15. Inhomogeneous boundary conditions

16. Wave motions on a string with a point load

17. A Green’s function approach

18. Excitation of a string by the impulsive stimulus of an attached load

19. Characteristic functions and complex eigenfrequencies

20. Resonant reflection and forced motion

Problems 1(a)

21. General excitation of string and oscillator

22. A string with two attached oscillators; matched inner and outer expansions

23. Instantaneous and moving point source functions

24. A densely loaded string

25. A composite or sectionally uniform string

26. Another composite string

27. A multi-section string

28. Initial and boundary value problems for a sectionally uniform string of finite length

29. Excitation of a string with variable length

Problems 1(b)

Part II

30. Interference

31. Energy density and flux

32. Energy propagation and the group velocity

33. Wave kinematics and dispersion

34. Stationary phase

35. An illustrative example

36. Extended initial profiles or ranges of support

37. An envelope of rays or caustic curve

38. Transformation and estimation of contour integrals near saddle points

39. Signal propagation and dispersion

40. Transient solutions of a dispersive wave equation and their ray representation

Problems 11(a)

41. Nonlinear equations for string motions; linearization and other aspects

42. Conservation relations and the pressure exerted by waves

43. Plane electromagnetic waves

44. Mechanical/electrical analogies and impedance concepts for wave propagation

45. Wave propagation along fluid boundaries

46. Source excited gravity waves on a fluid

47. Wave propagation in tubes having elastic walls

Problems 11(b)

48. Scattering matrices

49. A periodically loaded string

50. A periodic coefficient differential equation

51. Green’s functions and the periodically loaded string

52. Selective reflection

53. Average energy flux along the periodically loaded string

54. Forced and free motions of a regularly loaded string

55. Wave motions in a linear chain

56. Green’s functions for the linear chain and applications

57. Causality and dispersion relations

Problems 11(c)

Part III

58. A string with continuously variable density

59. An inhomogeneous segment

60. An inhomogeneous layer

61. Variable wave numbers with a periodic nature

62. Reflection from a periodically composed semi-infinite range

63. Variable wave number profiles with a discontinuous derivative or a null point

64. A multi-parameter family of smooth wave number profiles

65. Connection formulas and their applications

66. Approximate solutions of a wave-like nature for inhomogeneous settings

67. Improvements on the WKBJ or geometrical optics wave functions

68. Integral equation formulations and their consequences

69. Aspects of reflection for inhomogeneous settings

70. Phase calculations and turning points

71. Related equations and improved asymptotic solutions

72. Perturbation calculations in cases of non-uniformity

73. A short wave length expansion technique

74. Variational and other efficient characterizations of scattering coefficients

75. A scattering matrix and its variational characterization

76. Formalities of a variational calculation

77. A Green’s function representation and its variational characterization

78. Other inhomogeneous realizations

79. The Born approximation and reflection at short wave lengths

80. A long wave approximation

81. The Schrödinger wave equation and potential barrier problems

82. Inverse scattering theory

83. Variational theory and its implications

84. Progressive waves in variable configurations

85. A wave speed determination

86. Waves in a random setting

87. The dispersion relation and its role in stability/gain analysis

Problems III

Problems IV

References

Index

Unidirectional Wave Motions provides a comprehensive discussion of the formulations and their consequent elaborations which have found demonstrable value in wave analysis. The deliberate focus on unidirectional waves permits a relatively simple mathematical development, without leaving significant gaps in methodology and capability.
The book is organized into three parts. The first part deals with the particulars of individual wave equations; the geometry or kinematics of wave forms; and general matters bearing on the transport of energy and momentum as well as dispersion or frequency sensitivity. The second part focuses on aspects of wave generation by localized and extended sources. The third part examines the effects of interaction between specified primary waves and medium irregularities (e.g., obstacles, inclusions, or local variations in the material parameters). Information about these irregularities or scatterers, ranging from microscopic to terrestrial scales, may be gleaned through the attendant phenomena of reflection, refraction, and diffraction, which are fundamental to wave theory.