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You searched for subject:(DNLS). Showing records 1 – 3 of 3 total matches.

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University of Edinburgh

1. Moşincat, Răzvan Octavian. Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation.

Degree: PhD, 2018, University of Edinburgh

This thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial data in two settings: (i) on the torus (namely with the periodic boundary condition) and (ii) on the real line. Our first main goal is to study the global-in-time behaviour of solutions to DNLS in the periodic setting, where global well-posedness is known to hold under a small mass assumption. In Chapter 2, we relax the smallness assumption on the mass and establish global well-posedness of DNLS for smooth initial data. In Chapter 3, we then extend this result for rougher initial data. In particular, we employ the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao and show the global well-posedness of the periodic DNLS at the end-point regularity. In the implementation of the I-method, we apply normal form reductions to construct higher order modified energy functionals. In Chapter 4, we turn our attention to the uniqueness of solutions to DNLS on the real line. By using an infinite iteration of normal form reductions introduced by Guo, Kwon, and Oh in the context of one-dimensional cubic NLS on the torus, we construct solutions to DNLS without using any auxiliary function space. As a result, we prove the unconditional uniqueness of solutions to DNLS on the real line in an almost end-point regularity.

Subjects/Keywords: nonlinear Schro¨dinger equations; local well-posedness; DNLS

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APA (6th Edition):

Moşincat, R. O. (2018). Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/33244

Chicago Manual of Style (16th Edition):

Moşincat, Răzvan Octavian. “Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation.” 2018. Doctoral Dissertation, University of Edinburgh. Accessed February 22, 2020. http://hdl.handle.net/1842/33244.

MLA Handbook (7th Edition):

Moşincat, Răzvan Octavian. “Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation.” 2018. Web. 22 Feb 2020.

Vancouver:

Moşincat RO. Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation. [Internet] [Doctoral dissertation]. University of Edinburgh; 2018. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1842/33244.

Council of Science Editors:

Moşincat RO. Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation. [Doctoral Dissertation]. University of Edinburgh; 2018. Available from: http://hdl.handle.net/1842/33244

2. Law, Kody John Hoffman. Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials.

Degree: PhD, Mathematics, 2010, U of Massachusetts : PhD

The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potentials in 2(+1) dimensions. I will make predictions about these properties based on a discrete lattice model of coupled ordinary differential equations with the appropriate symmetry. The latter has been justified by Wannier function expansions in a so-called tight-binding approximation in the appropriate parametric regime. Numerical results for the full 2(+1)-D continuum model will be qualitatively compared with discrete model predictions as well as with nonlinear optics experiments in optically induced photonic lattices in photorefractive crystals. The predictions are also relevant for BECs (Bose-Einstein Condensates) in optical lattices. Advisors/Committee Members: Panayotis G. Kevrekidis, Nathaniel Whitaker, Hans Johnston.

Subjects/Keywords: DNLS; NLS; Non-square lattices; Nonlinear waves; Photonic lattices; Saturable nonlinearity; Mathematics; Statistics and Probability

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APA (6th Edition):

Law, K. J. H. (2010). Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials. (Doctoral Dissertation). U of Massachusetts : PhD. Retrieved from https://scholarworks.umass.edu/open_access_dissertations/179

Chicago Manual of Style (16th Edition):

Law, Kody John Hoffman. “Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials.” 2010. Doctoral Dissertation, U of Massachusetts : PhD. Accessed February 22, 2020. https://scholarworks.umass.edu/open_access_dissertations/179.

MLA Handbook (7th Edition):

Law, Kody John Hoffman. “Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials.” 2010. Web. 22 Feb 2020.

Vancouver:

Law KJH. Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials. [Internet] [Doctoral dissertation]. U of Massachusetts : PhD; 2010. [cited 2020 Feb 22]. Available from: https://scholarworks.umass.edu/open_access_dissertations/179.

Council of Science Editors:

Law KJH. Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials. [Doctoral Dissertation]. U of Massachusetts : PhD; 2010. Available from: https://scholarworks.umass.edu/open_access_dissertations/179

3. Faber, Felix. Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping.

Degree: The Institute of Technology, 2013, Linköping UniversityLinköping University

The purpose of this thesis is to study the effects of gain and damping on a nonlinear waveguide array with a strong disorder that is driven in the first site, and try to find regimes which have stable stationary solutions. This has been done with a modified DNLS (Discrete nonlinear Schrödinger equation). Stable stationary solutions were mainly found when the damping was stronger than the gain, but some stable stationary regimes were also found when the gain was stronger than the damping.

Subjects/Keywords: waveguide arrays; nonlinear; disorder; gain; damping; randomly distributed potentials; DNLS; Discrete nonlinear Schrödinger equation

…manifold of the stationary solutions for a random DNLS plotted against ω with h = G = 0, V = 1.9… …the manifold of the stationary solutions for a random DNLS plotted against ω with G = 0, V… …of the manifold of the stationary solutions for a random DNLS plotted against h with G = 0… …the first TP of the manifold of the stationary solutions for a random DNLS plotted against ω… …stationary solutions for a random DNLS plotted against h with ω = 0.2, G = 0.1, V = 1.9, n = 100… 

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APA (6th Edition):

Faber, F. (2013). Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping. (Thesis). Linköping UniversityLinköping University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-97496

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Faber, Felix. “Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping.” 2013. Thesis, Linköping UniversityLinköping University. Accessed February 22, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-97496.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Faber, Felix. “Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping.” 2013. Web. 22 Feb 2020.

Vancouver:

Faber F. Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping. [Internet] [Thesis]. Linköping UniversityLinköping University; 2013. [cited 2020 Feb 22]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-97496.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Faber F. Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping. [Thesis]. Linköping UniversityLinköping University; 2013. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-97496

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.