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  • 1.
    Nilson, Tomas
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Schiebold, Cornelia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego w Kielcach, Poland.
    Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour2018Report (Other academic)
    Abstract [en]

    The first main aim of this article is to derive an explicit solution formula for the scalar 2d-Toda lattice depending on three independent operator parameters, ameliorating work in [29]. This is achieved by studying a noncommutative version of the two-dimensional Toda lattice, generalizing its soliton solution to the noncommutative setting.

    The purpose of the applications part is to show that the family of solutions obtained from matrix data exhibits a rich variety of asymptotic behaviour. The first indicator is that web structures, studied extensively in the literature, see [4] and references therein, are a subfamily. Then three further classes of solutions (with increasingly unusual behaviour) are constructed, and their asymptotics are derived. 

  • 2.
    Porten, Egmont
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Boggess, Al
    Arizona State University, Tempe, AZ, U.S.A.
    Dwilewicz, Roman
    Cardinal Stefan Wyszy´nski University, Warsaw, Poland.
    On the Hartogs extension theorem for unbounded domains in Cn2018Report (Other academic)
    Abstract [en]

    Let Ω ⊂ Cn, n ≥ 2, be a domain with smooth connected boundary. IfΩ is relatively compact, the Hartogs-Bochner theorem ensures that everyCR distribution on ∂Ω has a holomorphic extension to Ω. For unboundeddomains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extensionproperty holds if and only if the envelope of holomorphy of Cn\Ω is Cn.It seems that it is a first result in the literature which gives a geometriccharacterization of unbounded domains in Cnfor which the Hartogs phenomenon holds. Comparing this to earlier work by the first two authorsand Z. S lodkowski, one observes that the extension problem sensitively depends on a finer geometry of the contact of a complex hypersurface andthe boundary of the domain.

  • 3.
    Schiebold, Cornelia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
    Asymptotics for the multiple pole solutions of the Nonlinear Schrödinger equation2014Report (Other academic)
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