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Self-Dual Nonlinear Schrödinger Equation

Title: The Self-Dual Nonlinear Schrödinger Equation: Properties and Dynamics.
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Name(s): Pawlak, Kelly, author
Department of Physics
Type of Resource: text
Genre: Text
Issuance: serial
Date Issued: 2014
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: We introduce a new nonlinear equation, the Self-Dual Nonlinear Schrödinger Equation (SDNLS) which resembles the Gross-Pitaevskii Equation [6] [4]. Unique to the SDNLS is its invariance under the Fourier transform — a form of duality which is reflected in systems such as the quantum harmonic oscillator. In this paper we explore various properties of the equation, starting with two proposed derivations based on known physics. We have managed to find a set of analytic time-independent solutions as well as a set of dynamical ones, which are presented in the paper. In addition to these we explore numerical solutions and comment on the qualitative behavior of these solutions in different parameter regimes. Finally, we make remarks regarding the future study of this equation. This thesis reflects a portion of a manuscript soon to be submitted to Physical Review A, entitled "Self-Dual Nonlocal Nonlinear Schrödinger Equation" in the upcoming months.
Identifier: FSU_migr_uhm-0335 (IID)
Keywords: NLS, Nonlinear Schrodinger, Self-Dual, Nonlinear Dynamics, Quantum, Partial Differential Equations, Applied Math, Physics
Submitted Note: A Thesis submitted to the Department of Physics and Astronomy in partial fulfillment of the requirements for graduation with Honors in the Major.
Degree Awarded: Spring Semester, 2014.
Date of Defense: March 28, 2014.
Subject(s): Condensed matter
Dynamics
Nonlinear systems
Optics
Differential equations
Physics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_uhm-0335
Restrictions on Access: http://creativecommons.org/licenses/by-nc-nd/4.0/
Owner Institution: FSU
Is Part of Series: Honors Theses.

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Pawlak, K. (2014). The Self-Dual Nonlinear Schrödinger Equation: Properties and Dynamics. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_uhm-0335