AMBROSE–SINGER THEOREM ON DIFFEOLOGICAL BUNDLES AND COMPLETE INTEGRABILITY OF THE KP EQUATION

DOI10.1142/S0219887813500436zbMath1278.58001arXiv1007.3543OpenAlexW2964126504MaRDI QIDQ2855844

Jean-Pierre Magnot

Publication date: 22 October 2013

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.3543

zbMATH Keywords

holonomyKP hierarchyinfinite-dimensional Lie groupsdiffeological spacesAmbrose-Singer theoremFrölicher Lie groups

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Topos-theoretic approach to differentiable manifolds (58A03)

Related Items (16)

On \(\mathrm{Diff}(M)\)-pseudo-differential operators and the geometry of non linear Grassmannians ⋮ Smooth constructions of homotopy-coherent actions ⋮ The diffeology of Milnor's classifying space ⋮ Frölicher structures, diffieties, and a formal KP hierarchy ⋮ On diffeological principal bundles of non-formal pseudo-differential operators over formal ones ⋮ Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups ⋮ On diffeologies from infinite dimensional geometry to PDE constrained optimization ⋮ Elastic diffeological spaces ⋮ On the domain of implicit functions in a projective limit setting without additional norm estimates ⋮ On diffeologies for power sets and measures ⋮ On the differential geometry of numerical schemes and weak solutions of functional equations ⋮ Hierarchies of holonomy groupoids for foliated bundles ⋮ The group of diffeomorphisms of a non-compact manifold is not regular ⋮ Hilbert series and moduli spaces of \(k U(N )\) vortices ⋮ On the Kadomtsev-Petviashvili hierarchy in an extended class of formal pseudo-differential operators ⋮ The Cauchy problem of the Kadomtsev-Petviashvili hierarchy with arbitrary coefficient algebra

Cites Work

• Unnamed Item
• Unnamed Item
• Complete integrability of the Kadomtsev-Petviashvili equation
• A Lie group structure for pseudodifferential operators
• Solvability of the super KP equation and generalized of the Birkhoff decomposition
• Structure groups and holonomy in infinite dimensions
• Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
• Algebras whose groups of units are Lie groups
• Integrals of nonlinear equations of evolution and solitary waves

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