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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 48, 1983 - Issue 6
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Original Articles

A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives

J.N.L. Connor Department of Chemistry, University of Manchester, Manchester, M13 9PL, England
,
P.R. Curtis Department of Chemistry, University of Manchester, Manchester, M13 9PL, England
&
D. Farrelly Department of Chemistry, University of Manchester, Manchester, M13 9PL, England; Joint Institute for Laboratory Astrophysics, National Bureau of Standards and University of Colorado, Boulder, Colorado, 80309, U.S.A.
Pages 1305-1330 | Received 19 Aug 1982, Accepted 09 Nov 1982, Published online: 22 Aug 2006

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R.A. Lee, D.F. Lynch & I.J. Wilson. (1985) Diffraction Patterns of Generalized Curvilinear Diffraction Gratings. Optica Acta: International Journal of Optics 32:5, pages 573-593.
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T. Uzer, J.T. Muckerman & M.S. Child. (1983) Collisions and umbilic catastrophes. Molecular Physics 50:6, pages 1215-1230.
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Articles from other publishers (36)

jinggui zhang, Yunwen Xu & Yajuan Tian. (2023) Acceleration-free propagation of Airy pulses in pure-quartic dispersion media. Journal of the Optical Society of America B.
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David Colas. (2020) Self-accelerating beam dynamics in the space fractional Schrödinger equation. Physical Review Research 2:3.
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Alessandro ZannottiAlessandro Zannotti. 2020. Caustic Light in Nonlinear Photonic Media. Caustic Light in Nonlinear Photonic Media 51 107 .
Chelo Ferreira, José L. López & Ester Pérez Sinusía. (2018) The asymptotic expansion of the swallowtail integral in the highly oscillatory region. Applied Mathematics and Computation 339, pages 837-845.
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Ke Cheng, Gang Lu & Xianqiong Zhong. (2017) The Poynting vector and angular momentum density of Swallowtail-Gauss beams. Optics Communications 396, pages 58-65.
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Riccardo Borghi. 2016. 1 70 .
Riccardo Borghi. (2012) Numerical computation of diffraction catastrophes with codimension eight. Physical Review E 85:4.
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Riccardo Borghi. (2011) Evaluation of cuspoid and umbilic diffraction catastrophes of codimension four. Journal of the Optical Society of America A 28:5, pages 887.
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Riccardo Borghi. (2010) On the numerical evaluation of umbilic diffraction catastrophes. Journal of the Optical Society of America A 27:7, pages 1661.
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Kenneth G. Kay. (2010) Semiclassical initial value treatment of wave functions. Chemical Physics 370:1-3, pages 51-61.
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Riccardo Borghi. (2008) On the numerical evaluation of cuspoid diffraction catastrophes. Journal of the Optical Society of America A 25:7, pages 1682.
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C.A. Hobbs, J.N.L. Connor & N.P. Kirk. (2007) Theory and numerical evaluation of oddoids and evenoids: Oscillatory cuspoid integrals with odd and even polynomial phase functions. Journal of Computational and Applied Mathematics 207:2, pages 192-213.
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J.F Nye. (2006) Dislocation lines in the swallowtail diffraction catastrophe. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463:2078, pages 343-355.
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A. S. Kryukovskii, D. S. Lukin, E. A. Palkin & D. S. Rastyagaev. (2006) Wave catastrophes: Types of focusing in diffraction and propagation of electromagnetic waves. Journal of Communications Technology and Electronics 51:10, pages 1087-1125.
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J.F Nye. (2006) Dislocation lines in the hyperbolic umbilic diffraction catastrophe. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462:2072, pages 2299-2313.
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Dario Amodei, Henk Keers, Don Vasco & Lane Johnson. (2006) Computation of uniform wave forms using complex rays. Physical Review E 73:3.
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Michael TrottMichael Trott. 2006. The Mathematica GuideBook for Numerics. The Mathematica GuideBook for Numerics 1 967 .
B. R. Fabijonas. (2004) Algorithm 838. ACM Transactions on Mathematical Software 30:4, pages 491-501.
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B. R. Fabijonas, D. W. Lozier & F. W. J. Olver. (2004) Computation of complex Airy functions and their zeros using asymptotics and the differential equation. ACM Transactions on Mathematical Software 30:4, pages 471-490.
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J F Nye. (2003) From Airy rings to the elliptic umbilic diffraction catastrophe. Journal of Optics A: Pure and Applied Optics 5:5, pages 503-510.
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Y. Elran & K. G. Kay. (2001) Uniform semiclassical IVR treatment of the S-matrix. The Journal of Chemical Physics 114:10, pages 4362-4376.
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Kenneth G. Kay. (2001) IVR Formulation of Miller's Correspondence Relations. The Journal of Physical Chemistry A 105:12, pages 2535-2545.
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Yu. A. Kravtsov & Yu. I. OrlovYu. A. Kravtsov & Yu. I. Orlov. 1999. Caustics, Catastrophes and Wave Fields. Caustics, Catastrophes and Wave Fields 48 72 .
M. Madhusoodanan & K. G. Kay. (1998) Globally uniform semiclassical wave functions for multidimensional systems. The Journal of Chemical Physics 109:7, pages 2644-2655.
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R. B. Paris. (1994) A Generalization of Pearcey’s Integral. SIAM Journal on Mathematical Analysis 25:2, pages 630-645.
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Yu. A. Kravtsov & Yu. I. OrlovYu. A. Kravtsov & Yu. I. Orlov. 1993. Caustics, Catastrophes and Wave Fields. Caustics, Catastrophes and Wave Fields 48 72 .
R.M. Corless, D.J. Jeffrey & H. Rasmussen. (1992) Numerical evaluation of airy functions with complex arguments. Journal of Computational Physics 99:1, pages 106-114.
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D. Kaminski. (1992) Asymptotics of the Swallowtail Integral Near the Cusp of the Caustic. SIAM Journal on Mathematical Analysis 23:1, pages 262-285.
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PHILIP L. MARSTON. 1992. 1 234 .
Andrzej Hanyga & Małgorzata Seredyńska. (1991) Diffraction of pulses in the vicinity of simple caustics and caustic cusps. Wave Motion 14:2, pages 101-121.
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Jakob J. Stamnes. (1989) Hybrid integration technique for efficient and accurate computation of diffraction integrals. Journal of the Optical Society of America A 6:9, pages 1330.
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Ngo Hoc, I. Besieris & M. Sockell. (1985) Phase-space asymptotic analysis of wave propagation in homogeneous dispersive and dissipative media. IEEE Transactions on Antennas and Propagation 33:11, pages 1237-1248.
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J. N. L. Connor & P. R. Curtis. (1984) Differential equations for the cuspoid canonical integrals. Journal of Mathematical Physics 25:10, pages 2895-2902.
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F. Wolf & H. J. Korsch. (1984) Fold and cusp catastrophe structures in rotational rainbow scattering. The Journal of Chemical Physics 81:7, pages 3127-3136.
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J N L Connor, P R Curtis & D Farrelly. (1984) The uniform asymptotic swallowtail approximation: practical methods for oscillating integrals with four coalescing saddle points. Journal of Physics A: Mathematical and General 17:2, pages 283-310.
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J. N. L. Connor, P. R. Curtis, C. J. Edge & A. Laganà. (1984) The uniform asymptotic swallowtail approximation: Application to the collinear H+F2 chemical reaction. The Journal of Chemical Physics 80:3, pages 1362-1363.
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