Tek, Süleyman2016-01-082016-01-082007http://hdl.handle.net/11693/14545Ankara : The Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 2007.Thesis (Ph.D.) -- Bilkent University, 2007.Includes bibliographical references leaves 93-96.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.viii, 96 leavesEnglishinfo:eu-repo/semantics/openAccessSoliton surfacesintegrable equationsshape equationWeingarten surfacesWillmore surfacesQC174.26.W28 T45 2007Solutions--Mathematics.Thesis