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Comparing the Variational Approximation and Exact Solutions of the Straight Unstaggered and Twisted Staggered Discrete Solitons

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Date Issued:
2016
Abstract/Description:
Discrete nonlinear Schr(&)#246;dinger 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.
Title: Comparing the Variational Approximation and Exact Solutions of the Straight Unstaggered and Twisted Staggered Discrete Solitons.
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Name(s): Marulanda, Daniel, Author
Kaup, David, Committee Chair
Moore, Brian, Committee Member
Vajravelu, Kuppalapalle, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2016
Publisher: University of Central Florida
Language(s): English
Abstract/Description: Discrete nonlinear Schr(&)#246;dinger 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.
Identifier: CFE0006350 (IID), ucf:51570 (fedora)
Note(s): 2016-08-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): Discrete nonlinear Schodinger equations -- Variational Approximation -- Straight unstaggered - twisted staggered discrete solitons
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0006350
Restrictions on Access: campus 2021-08-15
Host Institution: UCF

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