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

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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 (Campus-only Access)

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