2026-09-19T20:43:01Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/86924 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Jared Bronski Mizrak, Ozgur 2015-09-28T15:20:11Z 2015-09-28T15:20:11Z 10000-01-01 2009 2009 "We consider a class of nonlinear Schrodinger equations in N = 3, 4, 5 space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2( RN )) nonlinearities. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small initial data, converge to a nonlinear bound state. Therefore, the nonlinear bound states are asymptotically stable. The proof hinges on dispersive estimates that we obtain for the time dependent, Hamiltonian, linearized dynamics around a careful chosen one parameter family of bound states that ""shadows"" the nonlinear evolution of the system. Due to the generality of the methods we develop we expect them to extend to the case of perturbations of large bound states and to other nonlinear dispersive wave type equations." Made available in DSpace on 2015-09-28T15:20:11Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3363042.pdf: 983298 bytes, checksum: 5a1032b137a62940256ac1b8a397a746 (MD5) Previous issue date: 2009 Embargo set by: Seth Robbins for item 88205 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 91 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. http://hdl.handle.net/2142/86924 (MiAaPQ)AAI3363042 eng Mathematics Asymptotic Stability of the Ground States of the Nonlinear Schrodinger Equation text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.