Speaker
Michal Marvan
(Mathematical Institute in Opava)
Description
We shall explore a method, initiated by Guichard in 1890, which allows to generate sequences of Voss surfaces by quadratures, starting from an arbitrarily chosen pseudospherical surface and a seed solution of the Moutard equation, by means of two simple transformations. In this talk we
1) identify the Guichard transformations with the well-known mutually inverse recursion operators for symmetries of thesine-Gordon equation;
2) present a lemma which allows us to derive the length of Guichard's sequences from the invariance properties of the initial sine-Gordon solution;
3) introduce an extended class of inverted operators, increasing the number of Voss surfaces obtainable by quadratures.
A number of Voss nets will be presented explicitly.
