Abstract
A critical review of the literature on similarity solutions of nonlinear Schroedinger equations is presented. We demonstrate that the self-similar blow-up solutions discovered hitherto are all associated either with a simple stretching invariance, or with a slightly more complicated conformal invariance and generalizations of the latter. This generalized "quasi-invariance" reveals the nature of the blow-up singularity and resolves an old controversy. Most of the previous work has been done on the cubic nonlinearity. We generalize the results to an arbitrary power nonlinearity.
Original language | English |
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Journal | Physica Scripta |
Volume | 33 |
Issue number | 6 |
Pages (from-to) | 498-504 |
ISSN | 0031-8949 |
DOIs | |
Publication status | Published - 1986 |