Einstein, $\sigma$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation
Analysis of PDEs
2024-04-03 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Spectral Theory
Abstract
We present a non-isospectral GBDT version of B\"acklund-Darboux transformation for the gravitational and -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.
Keywords
Cite
@article{arxiv.2003.13024,
title = {Einstein, $\sigma$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:2003.13024},
year = {2024}
}
Comments
Section 4 of this paper is an important development of our work arXiv:math-ph/0703072. Some references and discussions are added in Section 4 of the second version