10 matching pages
Normal Forms Associated with Canonical Integrals: Cuspoid Catastrophe with Codimension… ►Special cases: , fold catastrophe; , cusp catastrophe; , swallowtail catastrophe. …
… ► …
Dislocation lines in the swallowtail diffraction catastrophe.
Proc. Roy. Soc. Lond. Ser. A 463, pp. 343–355.
§36.6 Scaling Relations…
6: 36.7 Zeros
A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives.
Molecular Phys. 48 (6), pp. 1305–1330.
A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey’s integral and its derivatives.
J. Phys. A 15 (4), pp. 1179–1190.
Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives.
Chem. Phys. Lett. 81 (2), pp. 306–310.
Catastrophes and molecular collisions.
Molecular Phys. 31 (1), pp. 33–55.
§36.11 Leading-Order Asymptotics… ►
… ►Define a mapping by relating to the normal form (36.2.1) of in the following way: …with the functions and determined by correspondence of the critical points of and . … ►This technique can be applied to generate a hierarchy of approximations for the diffraction catastrophes in (36.2.10) away from , in terms of canonical integrals for . For example, the diffraction catastrophe defined by (36.2.10), and corresponding to the Pearcey integral (36.2.14), can be approximated by the Airy function when is large, provided that and are not small. … ►For further information concerning integrals with several coalescing saddle points see Arnol’d et al. (1988), Berry and Howls (1993, 1994), Bleistein (1967), Duistermaat (1974), Ludwig (1966), Olde Daalhuis (2000), and Ursell (1972, 1980).