Binary Darboux transformations in bidifferential calculus and integrable reductions of vacuum Einstein equations

DOI10.3842/SIGMA.2013.009zbMath1384.37082arXiv1207.1308MaRDI QIDQ352461

Aristophanes Dimakis, Folkert Mueller-Hoissen

Publication date: 4 July 2013

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.1308

zbMATH Keywords

Einstein equationsbidifferential calculusbinary Darboux transformationblack ringchiral model

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Exact solutions to problems in general relativity and gravitational theory (83C15) Differential graded algebras and applications (associative algebraic aspects) (16E45) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (7)

A vectorial binary Darboux transformation for the first member of the negative part of the AKNS hierarchy ⋮ “Riemann equations” in bidifferential calculus ⋮ Self-consistent sources for integrable equations via deformations of binary Darboux transformations ⋮ Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras ⋮ NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks ⋮ Tropical limit of matrix solitons and entwining Yang-Baxter maps ⋮ Generalized Volterra lattices: binary Darboux transformations and self-consistent sources

This page was built for publication: Binary Darboux transformations in bidifferential calculus and integrable reductions of vacuum Einstein equations