Solution surfaces and surfaces from a variotional principle
Date
2007
Authors
Editor(s)
Advisor
Gürses, Metin
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Abstract
In this thesis, we construct 2-surfaces in R 3 and in three dimensional Minkowski space (M3). First, we study the surfaces arising from modified Korteweg-de Vries (mKdV), Sine-Gordon (SG), and nonlinear Schr¨odinger (NLS) equations in R 3 . Second, we examine the surfaces arising from Korteweg-de Vries (KdV) and Harry Dym (HD) equations in M3. In both cases, there are some mKdV, NLS, KdV, and HD classes contain Willmore-like and algebraic Weingarten surfaces. We further show that some mKdV, NLS, KdV, and HD surfaces can be produced from a variational principle. We propose a method for determining the parametrization (position vectors) of the mKdV, KdV, and HD surfaces.
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Degree Discipline
Mathematics
Degree Level
Doctoral
Degree Name
Ph.D. (Doctor of Philosophy)
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Language
English