Journal article
Blow-up in nonlinear Schroedinger equations. II. Similarity structure of the blow-up singularity
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.
Language: | English |
---|---|
Year: | 1986 |
Pages: | 498-504 |
ISSN: | 00318949 and 14024896 |
Types: | Journal article |
DOI: | 10.1088/0031-8949/33/6/002 |
ORCIDs: | Juul Rasmussen, Jens |