Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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 | References | Similar Articles | Additional Information

Abstract: The Lagrange manifold formalism is adapted to find asymptotic solutions for a class of hyperbolic systems near caustics.


References [Enhancements On Off] (What's this?)

  • [1] J. B. Keller, The geometrical theory of diffraction, Calculus of Variations and its Applications, McGraw-Hill, New York, 1958
  • [2] 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)
  • [3] R. M. Lewis and B. Granoff, Asymptotic theory of electromagnetic wave propagation is in an inhomogeneous plasma, Alta Frequenza 38, 51-59 (1969)
  • [4] 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)
  • [5] Robert M. Lewis, Asymptotic theory of wave-propagation, Arch. Rational Mech. Anal. 20 (1965), 191–250. MR 0184551, https://doi.org/10.1007/BF00276444
  • [6] Jack Indritz, Methods in analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0150991
  • [7] Arthur D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (1985), no. 6, 1404–1407. MR 790091, https://doi.org/10.1063/1.526954

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Additional Information

DOI: https://doi.org/10.1090/qam/1134752
Article copyright: © Copyright 1991 American Mathematical Society


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