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

Abstract

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.

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

References in corpus (2)

• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations in the low energy heterotic string effective theory

Cited by in corpus (1)

• On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory