Sigma model for Ernst equation: Lax representation, Bäcklund transformation and divergence-free currents
type: Item
instance of: scholarly article
title: Sigma model for Ernst equation: Lax representation, Bäcklund transformation and divergence-free currents
zbMATH Open document ID: 0554.35110
DOI: 10.1007/BF02083737
author: A. N. Tarakanov
author: E. V. Doktorov
published in: International Journal of Theoretical Physics
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 3882902
zbMATH Keywords: nonlinear equations
zbMATH Keywords: inverse scattering method
zbMATH Keywords: gauge equivalence
zbMATH Keywords: sigma model
zbMATH Keywords: Ernst equation
zbMATH Keywords: general relativity
zbMATH Keywords: Belinskij-Zakharov-type completely integrable equation
zbMATH Keywords: Lax representation
zbMATH Keywords: Bäcklund transformation
zbMATH Keywords: divergence-free currents
MaRDI profile type: Publication
cites work: Finite Lorentz transformations in quantum field theory
cites work: Q3864448
cites work: Some extremal problems in designing discriminating experiments
cites work: Gauge equivalence of exactly integrable field theoretic models
cites work: The Bäcklund transformations and the inverse scattering method of the Ernst equation.
cites work: Integrable Hamiltonian systems and interactions through quadratic constraints
cites work: Lie groups, spin equations, and the geometrical interpretation of solitons
cites work: Prolongation structures of nonlinear evolution equations
full work available at URL: https://doi.org/10.1007/bf02083737
OpenAlex ID: W2092833253
description: scientific article; zbMATH DE number 3882902