Similarity Structure of Wave-Collapse

Kristoffer Rypdal, Jens Juul Rasmussen, K. Thomsen

    Research output: Contribution to journalJournal articleResearchpeer-review


    Similarity transformations of the cubic Schrödinger equation (CSE) are investigated. The transformations are used to remove the explicit time variation in the CSE and reduce it to differential equations in the spatial variables only. Two different methods for similarity reduction are employed and the significance of similarity in the evolution of a collapsing wave packet is investigated. Numerical solutions in radial symmetry demonstrate that the similarity behaviour is local in space and time, and that some similarity solutions must be classified as improper solutions. The nature of the collapsing singularity is reexamined.
    Original languageEnglish
    JournalPhysica D: Nonlinear Phenomena
    Issue number3
    Pages (from-to)339-357
    Publication statusPublished - 1985


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