Integrable graded manifolds and nonlinear equations

DOI10.1007/BF01468141zbMath0588.17004MaRDI QIDQ1073162

Mikhail V. Saveliev

Publication date: 1984

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

zbMATH Keywords

Toda latticesine-Gordon equationLie superalgebrassupermanifoldsCartan elementintegrable embeddingssupersymmetrical Liouville equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Superalgebras (17A70) Graded Lie (super)algebras (17B70) Global submanifolds (53C40) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (7)

Lax type representation for embeddings of manifolds in non-Riemannian enveloping spaces ⋮ Nonlinear equations and graded Lie algebras ⋮ Classical and quantum extended superconformal algebra. ⋮ Multidimensional nonlinear systems related to the Grassmann manifolds BI, DI ⋮ Solution of the Cauchy problem for a continuous limit of the Toda lattice and its superextension ⋮ Exactly and completely integrable nonlinear dynamical systems ⋮ Supersymmetric integrable systems from geodesic flows on superconformal groups

Cites Work

• Two-dimensional exactly and completely integrable dynamical systems
• Supersymmetric two-dimensional Toda lattice
• Representation theory and integration of nonlinear spherically symmetric equations to gauge theories
• On reduction of a two-dimensional generalized Toda lattice to an ordinary differential equations system
• Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
• General solutions of nonlinear equations in the geometric theory of the relativistic string
• To a transformation theory of two-dimensional integrable systems
• SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH
• Lie superalgebras
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