Unidirectional Wave Motions

PrefaceIntroductionPart 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 IVReferencesIndex