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 form
ulations occur out of an associated cc ideal with different parametriz
ations 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 i
ntegrable gas dynamics system is presented.