Soliton geometry and the vacuum gravitational field equations

DOI10.1007/BF00401589zbMath0699.35240MaRDI QIDQ913151

Metin Gürses

Publication date: 1989

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse scattering methodLax pairszero curvaturesoliton connections

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Partial differential equations of mathematical physics and other areas of application (35Q99) Connections (general theory) (53C05) Riemann-Hilbert problems in context of PDEs (35Q15) Overdetermined systems of PDEs with variable coefficients (35N10)

Related Items (1)

New symmetries of the vacuum Einstein equations

Cites Work

• Solutions of Einstein's equations: techniques and results. Proceedings of the International Seminar on Exact Solutions of Einstein's Equations Held in Retzbach, Germany, November 14-18, 1983
• The soliton connection
• Cartan ideal, prolongation, and Bäcklund transformations for Einstein’s equations
• Inverse scattering problems in higher dimensions: Yang–Mills fields and the supersymmetric sine-Gordon equation
• Prolongation structures of nonlinear evolution equations

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