Blow-up in nonlinear Schroedinger equations. II. Similarity structure of the blow-up singularity

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    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 languageEnglish
    JournalPhysica Scripta
    Volume33
    Issue number6
    Pages (from-to)498-504
    ISSN0031-8949
    DOIs
    Publication statusPublished - 1986

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