THE AFFINSPHAREN EQUATION - MOUTARD AND BACKLUND-TRANSFORMATIONS

The affinspharen equation was introduced in 1953 in connection with a geometric problem posed earlier by Tzitzeica. It is here re-derived in a (1 + 1)-dimensional anisentropic gas dynamics context. A new linear representation is employed to show that alternative Monge-Ampere formulations occur out of an associated cc ideal with different parametrizations of its two-dimensional integral manifolds. Moutard and Backlund-type transformations are established. Tzitzeica surfaces are thereby constructed. In addition, a multi-parameter class of solutions of an integrable gas dynamics system is presented.