Abstract
In this chapter we analyze the explicit blowup solutions \(\psi _{R}^\mathrm{explicit}\).
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Notes
- 1.
This ODE describes self-similar collapse in the critical NLS (Sect. 11.1).
- 2.
Here by “blowup rate” we mean the rate at which \(L(z)\) goes to zero.
- 3.
See Sect. 23.9.1 for another example where the blowup rate has a discontinuity.
- 4.
- 5.
Here, by “generic” we refer to solutions of the critical NLS that undergo a stable collapse with (i) the asymptotic \(\psi _{R^{(0)}}\) profile at the loglog law rate (Sect. 14.6 and Chaps. 17 and 18), (ii) the asymptotic \(\psi _G\) profile at a square-root blowup rate (Chap. 19), and (iii) the asymptotic \(\psi _{G_m}\) vortex profile at a square-root blowup rate (Chap. 20).
- 6.
See Sect. 10.6.2.
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Fibich, G. (2015). The Explicit Critical Singular Peak-Type Solution \(\psi _{R}^\mathrm{explicit}\) . In: The Nonlinear Schrödinger Equation. Applied Mathematical Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-12748-4_10
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DOI: https://doi.org/10.1007/978-3-319-12748-4_10
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