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On global properties of solutions of some nonlinear Schrödinger-type equations

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dc.contributor.author Koo, Eva Hang
dc.date.accessioned 2012-07-25T22:53:43Z
dc.date.available 2012-07-25T22:53:43Z
dc.date.copyright 2012 en_US
dc.date.issued 2012-07-25
dc.identifier.uri http://hdl.handle.net/2429/42813
dc.description.abstract The Schrödinger equation, an equation central to quantum mechanics, is a dispersive equation which means, very roughly speaking, that its solutions have a wave-like nature, and spread out over time. We will consider global behaviour of solutions of two nonlinear variations of the Schrödinger equation. In particular, we consider the nonlinear magnetic Schrödinger equation. [Formulas omitted] We show that under suitable assumptions on the electric and magnetic potentials, if the initial data is small enough in H¹, then the solution of the above equation decomposes uniquely into a standing wave part, which converges as t → ∞, and a dispersive part, which scatters. We also consider the Schrödinger map equation into the 2-sphere. We obtain a global well-posedness result for this equation with radially symmetric initial data without any size restriction on the initial data. Our technique involves translating the Schrödinger map equation into a cubic, non-local Schrödinger equation via the generalized Hasimoto transform. There, we also show global well-posedness for the non-local Schrödinger equation with radially-symmetric initial data in the critical space L²(ℝ²), using the framework of Kenig-Merle and Killip-Tao-Visan. en_US
dc.language.iso eng en_US
dc.publisher University of British Columbia en
dc.title On global properties of solutions of some nonlinear Schrödinger-type equations en_US
dc.type Electronic Thesis or Dissertation en
dc.degree.name Doctor of Philosophy - PhD en_US
dc.degree.discipline Mathematics en_US
dc.degree.grantor University of British Columbia en
dc.date.graduation 2012-11 en_US
dc.degree.campus UBCV en_US
dc.description.scholarlevel Graduate en

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