Modified Korteweg-de Vries surfaces
Journal of Mathematical Physics
American Institute of Physics
013505-1 - 013505-16
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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.