arXiv subjects
Publications and source records attributed to Suleyman Tek.
In this work, we consider 2-surfaces in ${\mathbb R}^3$ arising from the modified Korteweg de Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV equation. mKdV surfaces contain Willmore-like and Weingarten surfaces. We show that some mKdV surfaces can be obtained from a variational principle where the Lagrange function is a polynomial of the Gaussian and mean curvatures.
We consider 2-surfaces arising from the Korteweg de Vries (KdV) equation. The surfaces corresponding to KdV are in a three dimensional Minkowski space. They contain a family of quadratic Weingarten and Willmore-like surfaces. We show that a subset of KdV surfaces can be obtained from a variational principle where the Lagrange function is a polynomial function of the Gaussian and mean curvatures. We finally give a method for constructing the surfaces explicitly, i.e., finding their parametrizations or finding their position vectors.