Abstract
In this chapter we consider the location of the singularity
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Notes
- 1.
\(Z_\mathrm{c}\) is also called the collapse distance, the blowup point, and the filamentation distance.
- 2.
\(Z_\mathrm{c}= \infty \) if \(\psi \) exists globally.
- 3.
We already derived this result from the dilation symmetry (Lemma 27.1).
- 4.
- 5.
The NGO method, which was used to derive (27.11), relies on this assumption.
- 6.
The value of \( Z_\mathrm{c}\) in (27.14) is half of that in [53], because the initial condition in [53] was \(\psi _0 = c e^{-\frac{r^2}{2}}\).
- 7.
PVC damage patterns from this experiment are presented in Fig. 25.2d–f.
- 8.
Varying \(\lambda \) and fixing \(P\) is equivalent to varying \(P\) and fixing \(\lambda \).
- 9.
See Sect. 36.2.4.
- 10.
A deformable mirror acts as a lens, except that the focused (or defocused) beam is reflected rather than transmitted.
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Fibich, G. (2015). Location of Singularity (\(Z_\mathrm{c}\)). In: The Nonlinear Schrödinger Equation. Applied Mathematical Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-12748-4_27
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DOI: https://doi.org/10.1007/978-3-319-12748-4_27
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