HETEROTIC LIOUVILLE SYSTEMS FROM THE BERNOULLI EQUATION

A new class of integrable two-dimensional partial differential equatio ns is constructed from the Bernoulli equation, called heterotic Liouvi lle systems due to the heterotic conformal symmetry. These systems are shown to possess infinitely many symmetries and are related to the su rfaces of non-constant Gauss curvatures in Euclidean three-space. The simplest nontrivial extension of the Liouville equation is just the he terotic Toda model gauging the Witt algebra found recently.