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Einstein, $σ$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation (2003.13024v2)
Published 29 Mar 2020 in math.AP, gr-qc, math-ph, math.MP, and math.SP
Abstract: We present a non-isospectral GBDT version of B\"acklund-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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