Einstein, $\sigma$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation

We present a non-isospectral GBDT version of Bäcklund–Darboux transformation for the gravitational and $\sigma$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix eigenvalues. An interesting integrable Ernst-type system, the auxiliary linear systems of which are non-isospectral canonical systems, is studied as well.

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Published 30 October 2023