# fold catastrophe

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## 5 matching pages

##### 1: 36.2 Catastrophes and Canonical Integrals
###### Normal Forms Associated with Canonical Integrals: Cuspoid Catastrophe with Codimension $K$
Special cases: $K=1$, fold catastrophe; $K=2$, cusp catastrophe; $K=3$, swallowtail catastrophe. …
##### 3: 36.4 Bifurcation Sets
###### Bifurcation (Catastrophe) Set for Umbilics
$K=1$, fold bifurcation set: …
##### 4: 36.10 Differential Equations
$K=1$, fold: (36.10.1) becomes Airy’s equation (§9.2(i))
36.10.3 $\frac{{\partial}^{2}\Psi_{1}}{{\partial x}^{2}}-\frac{x}{3}\Psi_{1}=0.$
$K=1$, fold: (36.10.6) is an identity. …
${\Phi_{s}}^{(\mathrm{U})}\left(s,t;\mathbf{x}\right)=\frac{\partial}{\partial s% }\Phi^{(\mathrm{U})}\left(s,t;\mathbf{x}\right),$
${\Phi_{t}}^{(\mathrm{U})}\left(s,t;\mathbf{x}\right)=\frac{\partial}{\partial t% }\Phi^{(\mathrm{U})}\left(s,t;\mathbf{x}\right).$
##### 5: 36.6 Scaling Relations
###### Diffraction Catastrophe Scaling
$\Psi_{K}(\mathbf{x};k)=k^{\beta_{K}}\Psi_{K}\left(\mathbf{y}(k)\right),$
$\Psi^{(\mathrm{U})}(\mathbf{x};k)=k^{\beta^{(\mathrm{U})}}\Psi^{(\mathrm{U})}% \left(\mathbf{y}^{(\mathrm{U})}(k)\right),$