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The Stability and Instabilities of S...

Segal, Benjamin L.

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The Stability and Instabilities of Stationary Solutions to the Nonlinear Schrodinger Equation and the Sine-Gordon Equation.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Stability and Instabilities of Stationary Solutions to the Nonlinear Schrodinger Equation and the Sine-Gordon Equation./
Author:	Segal, Benjamin L.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	116 p.
Notes:	Source: Dissertations Abstracts International, Volume: 79-03, Section: B.
Contained By:	Dissertations Abstracts International79-03B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10285732
ISBN:	9780355120394

The Stability and Instabilities of Stationary Solutions to the Nonlinear Schrodinger Equation and the Sine-Gordon Equation.
Segal, Benjamin L.

The Stability and Instabilities of Stationary Solutions to the Nonlinear Schrodinger Equation and the Sine-Gordon Equation. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 116 p.

Source: Dissertations Abstracts International, Volume: 79-03, Section: B.

Thesis (Ph.D.)--University of Washington, 2017.

This item must not be added to any third party search indexes.

I present an analysis of the stability spectrum of all stationary elliptic-type solutions to the focusing Nonlinear Schrodinger equation and the sine-Gordon equation. An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about the spectrum are derived. Specifically, the solution parameter space is shown to be split into regions of distinct qualitative behavior of the spectrum. Additional results on the stability of solutions with respect to perturbations of an integer multiple of the period are given, as well as a procedure for approximating the greatest real part of the spectrum.

ISBN: 9780355120394Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Elliptic solutions

The Stability and Instabilities of Stationary Solutions to the Nonlinear Schrodinger Equation and the Sine-Gordon Equation.
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100 1 $a Segal, Benjamin L. $3 3545128
245 1 4 $a The Stability and Instabilities of Stationary Solutions to the Nonlinear Schrodinger Equation and the Sine-Gordon Equation.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 116 p.
500 $a Source: Dissertations Abstracts International, Volume: 79-03, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Deconinck, Bernard.
502 $a Thesis (Ph.D.)--University of Washington, 2017.
506 $a This item must not be added to any third party search indexes.
506 $a This item must not be sold to any third party vendors.
520 $a I present an analysis of the stability spectrum of all stationary elliptic-type solutions to the focusing Nonlinear Schrodinger equation and the sine-Gordon equation. An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about the spectrum are derived. Specifically, the solution parameter space is shown to be split into regions of distinct qualitative behavior of the spectrum. Additional results on the stability of solutions with respect to perturbations of an integer multiple of the period are given, as well as a procedure for approximating the greatest real part of the spectrum.
590 $a School code: 0250.
650 4 $a Applied Mathematics. $3 1669109
653 $a Elliptic solutions
653 $a Focusing NLS
653 $a Sine-Gordon
653 $a Stability
690 $a 0364
710 2 $a University of Washington. $b Applied Mathematics. $3 3283946
773 0 $t Dissertations Abstracts International $g 79-03B.
790 $a 0250
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10285732