Abstract
In this chapter we consider peak-type blowup solutions of the supercritical NLS
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Notes
- 1.
This is similar to the critical case, where the monotone \({R^{(0)}}\) profile is an attractor for the self-similar profile (Chap. 14), but the non-monotone, excited-state \({R^{(n)}}\) profiles are unstable (Sect. 10.6.3). It is also “similar” to the explicit singular ring-type solutions \(\psi _G^\mathrm{{explicit}}\) of the critical NLS, where the single-ring solution is stable but the multi-rings solutions are unstable (Sect. 11.4.1). In that case, the single-ring solution is the “least non-monotone” (single- or multi-) ring profiles.
- 2.
See Sect. 12.6.
- 3.
The function \(L(z)\) can be extracted from the NLS solution \(\psi \) using relation (21.14).
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Fibich, G. (2015). Singular \(H^1\) Peak-Type Solutions \(\big (\psi _Q\big )\) . In: The Nonlinear Schrödinger Equation. Applied Mathematical Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-12748-4_21
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DOI: https://doi.org/10.1007/978-3-319-12748-4_21
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