Sigma model for Ernst equation: Lax representation, Bäcklund transformation and divergence-free currents
It has been shown recently that there exists a relation between some nonlinear equations solvable by the inverse scattering method. This fact is expressed by the notion of gauge equivalence and leads to the existence of a sigma model associated with the given nonlinear equation. In the present paper a sigma model associated with the Ernst equation of general relativity is obtained. This model is described by the Belinskij- Zakharov-type completely integrable equation and is formally equivalent to the usual sigma model in curved two-dimensional space. The corresponding Lax representation, Bäcklund transformation, and divergence-free currents are obtained.
Belinskij-Zakharov-type completely integrable equation
scientific article; zbMATH DE number 3882902