On caustics associated with hyperbolic systems
Author:
Arthur D. Gorman
Journal:
Quart. Appl. Math. 49 (1991), 773-780
MSC:
Primary 58G16; Secondary 35C20, 35L40
DOI:
https://doi.org/10.1090/qam/1134752
MathSciNet review:
MR1134752
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Abstract: The Lagrange manifold formalism is adapted to find asymptotic solutions for a class of hyperbolic systems near caustics.
J. B. Keller, The geometrical theory of diffraction, Calculus of Variations and its Applications, McGraw-Hill, New York, 1958
B. Granoff and R. M. Lewis, Asymptotic solution of initial boundary-value problems for hyperbolic systems, Philos. Trans. Roy. Soc. London Ser. A 262, 381–411 (1967)
R. M. Lewis and B. Granoff, Asymptotic theory of electromagnetic wave propagation is in an inhomogeneous plasma, Alta Frequenza 38, 51–59 (1969)
A. D. Gorman and R. Wells, A sharpening of Maslov’s method of characteristics to give the full asymptotic series, Quart. Appl. Math. 40 (2), 159–163 (1982)
- Robert M. Lewis, Asymptotic theory of wave-propagation, Arch. Rational Mech. Anal. 20 (1965), 191–250. MR 184551, DOI https://doi.org/10.1007/BF00276444
- Jack Indritz, Methods in analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0150991
- Arthur D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (1985), no. 6, 1404–1407. MR 790091, DOI https://doi.org/10.1063/1.526954
J. B. Keller, The geometrical theory of diffraction, Calculus of Variations and its Applications, McGraw-Hill, New York, 1958
B. Granoff and R. M. Lewis, Asymptotic solution of initial boundary-value problems for hyperbolic systems, Philos. Trans. Roy. Soc. London Ser. A 262, 381–411 (1967)
R. M. Lewis and B. Granoff, Asymptotic theory of electromagnetic wave propagation is in an inhomogeneous plasma, Alta Frequenza 38, 51–59 (1969)
A. D. Gorman and R. Wells, A sharpening of Maslov’s method of characteristics to give the full asymptotic series, Quart. Appl. Math. 40 (2), 159–163 (1982)
R. M. Lewis, Asymptotic theory of wave propagation, Arch. Rational Mech. Anal. 20, 191–250 (1965)
J. Indritz, Methods in Analysis, Macmillan, New York, 1963
A. D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (6), 1404–1407 (1985)
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Article copyright:
© Copyright 1991
American Mathematical Society
