Soliton yüzeyleri ve varyasyonel prensibinden çıkan yüzeyler

In this thesis, we construct 2-surfaces in R3 and in three dimensional Minkowskispace (M3 ). First, we study the surfaces arising from modified Korteweg-de Vries(mKdV), Sine-Gordon (SG), and nonlinear Schrüdinger (NLS) equations in R3 .oSecond, we examine the surfaces arising from Korteweg-de Vries (KdV) and HarryDym (HD) equations in M3 . In both cases, there are some mKdV, NLS, KdV, andHD classes contain Willmore-like and algebraic Weingarten surfaces. We furthershow that some mKdV, NLS, KdV, and HD surfaces can be produced from avariational principle. We propose a method for determining the parametrization(position vectors) of the mKdV, KdV, and HD surfaces.Keywords: Soliton surfaces, Willmore surfaces, Weingarten surfaces, shape equa-tion, integrable equations.i