►Figure 36.3.1: Modulus of Pearcey integral .
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Figure 36.3.2: Modulus of swallowtail canonical integral function .
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Figure 36.3.3: Modulus of swallowtail canonical integral function .
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Figure 36.3.4: Modulus of swallowtail canonical integral function .
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Scales were corrected in all figures. The interval
was replaced by and replaced by . All plots and interactive visualizations were regenerated to improve image quality.
(a) Density plot.
(b) 3D plot.
Figure 36.3.9: Modulus of hyperbolic umbilic canonical integral function
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(a) Density plot.
(b) 3D plot.
Figure 36.3.10: Modulus of hyperbolic umbilic canonical integral function
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(a) Density plot.
(b) 3D plot.
Figure 36.3.11: Modulus of hyperbolic umbilic canonical integral function
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(a) Density plot.
(b) 3D plot.
Figure 36.3.12: Modulus of hyperbolic umbilic canonical integral function
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►A relativistic treatment becoming necessary as becomes large as corrections to the non-relativistic Schrödinger picture are of approximate order , being the dimensionless fine structure constant , where is the speed of light.
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►The Stokes set consists of the rays in the complex -plane.
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►For , there are two solutions , provided that .
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►This consists of three separate cusp-edged sheets connected to the cusp-edged sheets of the bifurcation set, and related by rotation about the -axis by .
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§36.5(iv) Visualizations
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►►►Figure 36.5.8: Sheets of the Stokes surface for the elliptic umbilic catastrophe (colored and with mesh) and the bifurcation set (gray).
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