ON A 2-DIMENSIONAL INTEGRABLE ERNST-TYPE EQUATION(1)

A strong 2+1-dimensional integrable extension of Ernst's equation of g eneral relativity is proposed. Its richness is demonstrated by means o f various canonical dimensional reductions and specializations which l ead to formal analogues of well-known 1+1- and 2+1-dimensional integra ble systems such as the self-induced transparency equations, the Konop elchenko-Rogers equations, a 2+1-dimensional Darboux system descriptiv e of conjugate coordinate systems, a single 2+1-dimensional sine-Gordo n equation and the equations representing its Backlund transformation. A Darboux-Levi-type transformation is given and its compatibility wit h the above-mentioned reductions is shown.