Abstract
A strong 2+1-dimensional integrable extension of Ernst’s equation of general relativity is proposed. Its richness is demonstrated by means of various canonical dimensional reductions and specializations which lead to formal analogues of well-known 1+1- and 2+1-dimensional integrable systems such as the self-induced transparency equations, the Konopelchenko-Rogers equations, a 2+1- dimensional Darboux system descriptive of conjugate coordinate systems, a single 2+1-dimensional sine-Gordon equation and the equations representing its Bäcklund transformation. A Darboux-Levi-type transformation is given and its compatibility with the above-mentioned reductions is shown.
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