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Front Cover; Asymptotic Wave Theory; Copyright Page; Preface; Table of Contents; CHAPTER 1. THE FOURIER-LAPLACE INTEGRAL; 1.1. The Laplace transform; 1.2. The Fourier transform in L1; 1.3. The Fourier transform in L2; 1.4. The Laplace transform (continued); 1.5. The Mellin transform; CHAPTER 2. SPECIAL FUNCTIONS; 2.I. The gamma function; 2. II. The Bessel functions; CHAPTER 3. THE WAVE EQUATION; 3.1. Introduction; 3.2. The reflexion and refraction of a plane wave at the interface between two homogeneous media; 3.3. Spherical waves; 3.4. Cylindrical waves; 3.5. Group velocity; 3.6. Wave guide
3.7. Successive reflexions of plane waves at two parallel rigid planes3.8. The relation between spherical and plane waves; 3.9. The reflexion of a spherical wave at a plane interface; 3.10. An alternative approach to Weyl's formula. Poritsky's generalisation; CHAPTER 4. ASYMPTOTIC METHODS; 4.1. Asymptotic expansion; 4.2. The asymptotic expansion of Hankel's functions in the neighborhood of the point at infinity; 4.3. The Laplace method; 4.4. Asymptotic relations and Laplace's transform; 4.5. The Laplace method (continued); 4.6. The method of steepest descent
4.7. Waves in linear dispersive media4.8. The asymptotic representation of the reflected wave in the problem of a spherical wave impinging on a plane interface. The lateral wave; 4.9. The method of steepest descent; an extension to the case when some pole is located near the saddle; 4.10. The asymptotic representation of Hankel's functions of large order; 4.11. An asymptotic representation of Legendre's functions of large order; 4.12. The asymptotic representation of Hankel's functions of large order (continued); CHAPTER 5. SCATTERING MATRIXTHEORY; 5.1. Introduction; 5.I. The direct problem
5. II. The inverse problemCHAPTER 6. FLOW IN OPEN CHANNEL; ASYMPTOTIC SOLUTION OF SOME LINEAR AND NON-LINEAR WAVE EQUATIONS; 6.I. The kinematics and dynamics of flow in open channel; 6. II. The asymptotic representation of the solution of the wave equation; 6. III. Non-linear wave theory; CHAPTER 7. SEISMIC WAVES; 7.1. Waves in elastic solids; 7.2. Plane waves; 7.3. Reflexion and refraction of plane elastic waves; 7.4. Waves of kind I, II, III; 7.5. Analytic representation of P and S waves; 7.6. The layered spherical model; 7.7. The energy balance
7.8. The reflexion and transmission coefficients7.9. The wave system in the layered spherical model; 7.10. The P, PcP, PcS, PKP waves produced by a point source located outside the core; 7.11. Application of the method of steepest descent to P and PcP wave integrals; 7.12. The diffracted PcP wave; CHAPTER 8. SOME PROBLEMS IN WATER WAVE THEORY; Introduction; 8.I. Oscillations in an infinite channel of variable depth; 8. II. A diffraction problem; REFERENCES; INDEX
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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Includes bibliographical references (pages 345-347) and index.
Amsterdam : North-Holland Pub. Co. ; New York : American Elsevier Pub. Co., 1976
North-Holland series in applied mathematics and mechanics ; v. 20