Two-dimensional nonlinear string-type equations and their exact integration

DOI10.1007/BF00405873zbMath0533.35077OpenAlexW2042253696MaRDI QIDQ789615

A. N. Leznov, Mikhail V. Saveliev

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1007/bf00405873

zbMATH Keywords

Toda latticenonlinear dynamical systemsexact integrationgraded Lie algebraGoursat problemLax-type representationnonlinear string-type equations

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Partial differential equations of mathematical physics and other areas of application (35Q99) Dynamical systems and ergodic theory (37-XX)

Related Items (6)

Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. I ⋮ Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. II: A nonlinear system arising from the group \(G_{6,1}\) and its exact integration ⋮ Integration of the \(\text{SL}(2,{\mathbb{R}})/\text{U}(1)\) gauged WZNW model with periodic boundary conditions ⋮ Two-dimensional exactly and completely integrable dynamical systems ⋮ Reduction in the model of a relativistic string for arbitrary dimension of Minkowski space ⋮ Quantization and representation theory of finite \(W\) algebras

Cites Work

• Representation of zero curvature for the system of nonlinear partial differential equations \(x_{\alpha,z\bar z}=\exp(kx)_\alpha\) and its integrability
• Representation theory and integration of nonlinear spherically symmetric equations to gauge theories
• Unified approach to strings and vortices with soliton solutions

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