Abstract
Discrete nonlinear Schrödinger equations (DNSL) have been used to provide models of a variety of physical settings. An application of DNSL equations is provided by Bose-Einstein condensates which are trapped in deep optical-lattice potentials. These potentials effectively splits the condensate into a set of droplets held in local potential wells, which are linearly coupled across the potential barriers between them [3]. In previous works, DNLS systems have also been used for symmetric on-site-centered solitons [11]. A few works have constructed different discrete solitons via the variational approximation (VA) and have explored their regions for their solutions [11, 12]. Exact solutions for straight unstaggered-twisted staggered (SUTS) discrete solitons have been found using the shooting method [12]. In this work, we will use Newton's method, which converges to the exact solutions of SUTS discrete solitons. The VA has been used to create starting points. There are two distinct types of solutions for the soliton's waveform: SUTS discrete solitons and straight unstaggered discrete solitons, where the twisted component is zero in the latter soliton. We determine the range of parameters for which each type of solution exists. We also compare the regions for the VA solutions and the exact solutions in certain selected cases. Then, we graphically and numerically compare examples of the VA solutions with their corresponding exact solutions. We also find that the VA provides reasonable approximations to the exact solutions.
Notes
If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu
Graduation Date
2016
Semester
Summer
Advisor
Kaup, David
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematical Science
Format
application/pdf
Identifier
CFE0006350
URL
http://purl.fcla.edu/fcla/etd/CFE0006350
Language
English
Release Date
August 2021
Length of Campus-only Access
5 years
Access Status
Masters Thesis (Open Access)
STARS Citation
Marulanda, Daniel, "Comparing the Variational Approximation and Exact Solutions of the Straight Unstaggered and Twisted Staggered Discrete Solitons" (2016). Electronic Theses and Dissertations. 5224.
https://stars.library.ucf.edu/etd/5224