Canonical functions of asymptotic diffraction theory associated with symplectic singularities

• Autorzy: Andrzej Hanyga
• Języki publikacji: EN

Abstrakty

EN

A general method of deriving canonical functions for ray field singularities involving caustics, shadow boundaries and their intersections is presented. It is shown that many time-domain canonical functions can be expressed in terms of elementary functions and elliptic integrals.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 39
• Numer: 1
• Strony: 57-71

Daty

wydano

1997

Twórcy

autor

Andrzej Hanyga

• Institute for Solid Earth Physics, University of Bergen Allégaten 41, N-5007 Bergen, Norway

Bibliografia

• [1] V. I. Arnol'd, A. N. Varchenko and S. M. Husein-Zade, Singularities of Differentiable Maps, Vol. I, Birkhäuser Verlag, Basel, 1985.
• [2] S. Benenti and W. M. Tulczyjew, The Geometrical Meaning and Globalization of the Hamilton-Jacobi Method, in: Differential geometrical methods in mathematical physics, Proc. Conf. Aix-en-Provence/Salamanca 1979, Lecture Notes in Math. 836, Springer, Berlin, 1980, 9-21.
• [3] M. G. Brown and F. D. Tappert, Causality, caustics and the structure of transient wavefields, J. Acoust. Soc. Amer. 85 (1986), 251-255.
• [4] R. Burridge, The reflection of a pulse in a solid sphere, Proc. Roy. Soc. London A276 (1962), 367-400.
• [5] J. N. L. Connor, A method for the numerical evaluation of the oscillatory integrals associated with cuspoid catastrophes: applications to Pearcey's integral and its derivatives, J. Phys. A 15 (1982), 1179-1190.
• [6] J. J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math. 27 (1974), 207-281.
• [7] M. V. Fedoryuk, Saddle Point Method, Nauka, Moscow, 1977 (in Russian).
• [8] M. Golubitsky and V. Guillemin, Stable Mappings and their Singularities, Springer-Verlag, New York, 1973.
• [9] V. Guillemin and S. Sternberg, Geometric Asymptotics, American Mathematical Society, Providence, RI, 1977.
• [10] A. Hanyga, Boundary effects in Asymptotic Diffraction Theory, Part I-III, Seismo-series (int. reports ISEP Univ. of Bergen), Vol. 35-37, Bergen, 1989.
• [11] A. Hanyga, Local behaviour of wavefields at simple caustics, Seismo-series (int. reports ISEP Univ. of Bergen), Vol. 38, 1989.
• [12] A. Hanyga, Numerical applications of Asymptotic Diffraction Theory, in: Mathematical and Numerical Aspects of Wave Propagation, Univ. of Delaware, June 1993, R. Kleinman et al. (eds.), SIAM, Philadelphia, 1993.
• [13] A. Hanyga, Asymptotic Diffraction Theory applied to edge-vertex diffraction, in: Proc. 7th Conference on Waves and Stability in Continuous Media, Bologna, Nov. 1993, S. Rionero & T. Ruggeri (eds.), World Scientific Publishing, Singapore, 1994.
• [14] A. Hanyga, Asymptotic vertex and edge diffraction, Geophys. J. Int. 122 (1995), 277-290.
• [15] A. Hanyga and M. Seredyńska, Diffraction of pulses in the vicinity of simple caustics and caustic cusps, Wave Motion 14 (1991), 101-121.
• [16]S. Janeczko, On isotropic submanifolds and evolution of quasi-caustics, Pacific J. Math. 158 (1993), 317-334.
• [17] S. Janeczko and G. Plotnikova, Sur la structure de quasi-caustiques en diffraction géometrique, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 543-546.
• [18] J. B. Keller, Geometrical Theory of Diffraction, J. Opt. Soc. Amer. 52 (1966), 116-130.
• [19] Yu. A. Kravtsov and Yu. I. Orlov, Caustics, Catastrophes and Wave Fields, Springer-Verlag, Berlin, 1993.
• [20] V. P. Maslov and V. M. Fedoryuk, Semi-classical approximation in quantum mechanics, D. Reidel, Doordrecht, 1981.
• [21] F. Pham, Singularités des systèmes differentiels de Gauss-Manin, Progr. Math. 2, Birkhäuser, Basel, 1979.
• [22] T. Poston and I. Stewart, Catastrophe Theory and Its Applications, Pitman, London, 1978.
• [23] D. Siersma, Singularities of functions on boundaries, corners etc., Quart. J. Math. Oxford (2) 32 (1981), 119-127.
• [24] D. Stickler, D. S. Ahluwalia and L. Ting, Application of Ludwig's uniform progressing wave ansatz to a smooth caustic, J. Acoust. Soc. Amer. 69 (1981), 1673-1681.
• [25] A. Weinstein, Lectures on Symplectic Manifolds, in: CBMS Conference Series, American Mathematical Society, Vol. 29, Providence, RI, 1977.