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Kirr, Eduard-Wilhelm Bronski, Jared C. Zharnitsky, Vadim Kirr, Eduard-Wilhelm Laugesen, Richard S. Skulkhu, Ruth 2012-06-27T21:32:05Z 2014-06-28T10:00:29Z 2012-05 2012-06-27T21:32:05Z 2012-05 In this thesis we obtained new results on the asymptotic stability of ground states of the nonlinear Schrödinger equation in space dimension two. Under our hypotheses, the result actually shows asymptotic completeness in the regime of small initial data, i.e. any small initial data evolves into a superposition of a solitary wave (ground state) and a radiative part that decays in time. Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2012-04-18T20:01:12Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Skulkhu_Ruth.pdf: 568028 bytes, checksum: 7653d6288b5129bf6a38a4194d7aaed6 (MD5) Made available in DSpace on 2012-06-27T21:32:05Z (GMT). No. of bitstreams: 2 Skulkhu_Ruth.pdf: 568028 bytes, checksum: 7653d6288b5129bf6a38a4194d7aaed6 (MD5) license.txt: 4061 bytes, checksum: cb2fcab20644c4d5969403e088716b59 (MD5) Item marked as restricted to the 'Administrator' Group (id=1) by William Ingram (wingram2@illinois.edu) on 2012-06-27T21:32:51Z Item is restricted until 2014-06-27T21:32:23Z Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2014-06-28T10:00:29Z Item was in collections: Graduate Theses and Dissertations at Illinois (ID: 204) No. of bitstreams: 2 Skulkhu_Ruth.pdf: 568028 bytes, checksum: 7653d6288b5129bf6a38a4194d7aaed6 (MD5) license.txt: 4061 bytes, checksum: cb2fcab20644c4d5969403e088716b59 (MD5) Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2014-06-28T10:00:29Z http://hdl.handle.net/2142/32082 en © 2012 by Ruth J. Skulkhu. All rights reserved. Mathematics Partial Differential Equations Schrödinger Equation Nonlinear Completeness Asymptotic Stability Asymptotic stability and completeness in 2D nonlinear Schrodinger equation text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD