Speaker
Wolfgang Karl Schief
(University of New South Wales)
Description
We present a framework in three-dimensional Minkowski space $\mathbb{R}^{1,2}$ which unifies the extended Dym, KdV, modified KdV and modified modified KdV equations via parallel, offset and midsurfaces. Each equation governs a class of surfaces, the members of which are foliated by geodesics of certain properties. These classes of surfaces are linked by reciprocal and Miura-type transformations. In particular, we obtain a novel geometric interpretation of the classical Miura transformation linking the KdV and mKdV equations. In total, there exist ten classes which may be associated both combinatorially and literally with the 4 vertices and 6 midpoints of the edges of a (moving) tetrahedron.
