Browsing by Subject "Weingarten surfaces"

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    Solution surfaces and surfaces from a variotional principle
    (2007) Tek, Süleyman
    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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    Weingarten surfaces arising from soliton theory
    (1999) Ceyhan, Özgür
    In this work we presented a method for constructing surfaces in associated with the symmetries of Gauss-Mainardi-Codazzi equations. We show that among these surfaces the sphere has a unique role. Under constant gauge transformations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by symmetries of the sine-Gordon equation are homeomorphic to sphere. We also construct some Weingarten surfaces arising from the deformations of sine-Gordon, sinh-Gordon, nonlinear Schrödinger and modified Korteweg-de Vries equations.