mKdV Surfaces

Details mKdV Surfaces mKdV Surfaces

2006-12-25

arxiv.org/abs/math-ph/0612076v3

J.Math.Phys.48:013505,2007

Physics

Mathematical Physics

24 pages

Scientific paper

10.1063/1.2409523

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.

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