Browsing by Subject "Soliton Surfaces"

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    Korteweg-de Vries surfaces
    (Elsevier, 2014-01) Gurses, M.; Tek, S.
    We consider 2-surfaces arising from the Korteweg-de Vries (KdV) hierarchy and the KdV equation. The surfaces corresponding to the KdV equation are in a three-dimensional Minkowski (M3) space. They contain a family of quadratic Weingarten and Willmore-like surfaces. We show that some KdV surfaces can be obtained from a variational principle where the Lagrange function is a polynomial function of the Gaussian and mean curvatures. We also give a method for constructing the surfaces explicitly, i.e., finding their parameterizations or finding their position vectors.© 2013 Elsevier Ltd. All rights reser.
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    Modified Korteweg-de Vries surfaces
    (American Institute of Physics, 2007) Tek, S.
    In this work, we consider 2-surfaces in R3 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. © 2007 American Institute of Physics.