dc.contributor.advisor Stanislavova, Milena dc.contributor.author Feng, Wen dc.date.accessioned 2019-05-18T19:24:12Z dc.date.available 2019-05-18T19:24:12Z dc.date.issued 2018-08-31 dc.date.submitted 2018 dc.identifier.other http://dissertations.umi.com/ku:16099 dc.identifier.uri http://hdl.handle.net/1808/27997 dc.description.abstract In this work, we present analytical studies of standing waves in three NLS models. We first consider the spectral stability of ground states of fourth order semi-linear Schrödinger and Klein-Gordon equations and semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion. We use Hamiltonian index counting theory, together with the information from a variational construction to develop sharp conditions for spectral stability for these waves. The second case is about the existence and the stability of the vortices for the NLS in higher dimensions. We extend the existence and stability results of Mizumachi from two-space dimensions to $n$ space dimensions. Finally, the third equation we consider is a nonlocal NLS which comes from modeling nonlinear waves in Parity-time symmetric systems. Here again, we investigate the spectral stability of standing waves of its $\mathcal{PT}$ symmetric solutions. dc.format.extent 90 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject Existence dc.subject NLS dc.subject Spectral Stability dc.subject Standing Waves dc.title Analytical studies of standing waves in three NLS models dc.type Dissertation dc.contributor.cmtemember Stanislavova, Milena dc.contributor.cmtemember Chen, Geng dc.contributor.cmtemember Johnson, Mat dc.contributor.cmtemember Kong, Man dc.contributor.cmtemember Stefanov, Atanas dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel Ph.D. dc.identifier.orcid dc.rights.accessrights openAccess
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