Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups

DOI10.1007/s00023-020-00896-3zbMath1447.35287arXiv1608.03994OpenAlexW3010046260WikidataQ115389932 ScholiaQ115389932MaRDI QIDQ2191065

Enrique G. Reyes, Jean-Pierre Magnot

Publication date: 23 June 2020

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.03994

zbMATH Keywords

Kadomtsev-Petviashvili hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Yang-Mills and other gauge theories in quantum field theory (81T13) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) 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 infinite-dimensional Lie algebras and other algebraic structures (37K30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

On (t2, t3)-Zakharov–Shabat equations of generalized Kadomtsev–Petviashvili hierarchies ⋮ Smooth constructions of homotopy-coherent actions ⋮ Frölicher structures, diffieties, and a formal KP hierarchy ⋮ On diffeological principal bundles of non-formal pseudo-differential operators over formal ones ⋮ Lie bialgebroid of pseudo-differential operators ⋮ On diffeologies from infinite dimensional geometry to PDE constrained optimization ⋮ Diffeologies and generalized Kadomtsev-Petviashvili hierarchies ⋮ A Kadomtsev-Petviashvili hierarchy driven by equation manifolds ⋮ On the differential geometry of numerical schemes and weak solutions of functional equations ⋮ 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 ⋮ On the geometry of $Diff(S^1)$-pseudodifferential operators based on renormalized traces.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups
• Symplectic leaves of the Gel'fand-Dikij brackets and homotopy classes of nondegenerate curves
• Hamiltonian structure of M. Sato's hierarchy of Kadomtsev-Petviashvili equation
• What is a classical r-matrix?
• Towards a Lie theory of locally convex groups
• Hamiltonian structure of Sato's hierarchy of KP equations and a coadjoint orbit of a certain formal Lie group
• Complete integrability of the Kadomtsev-Petviashvili equation
• A Lie group structure for pseudodifferential operators
• A Lie group structure for Fourier integral operators
• Characterization of Jacobian varieties in terms of soliton equations
• Solvability of the super KP equation and generalized of the Birkhoff decomposition
• Reduction of Hamiltonian systems, affine Lie algebra, and Lax equations. II
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Noncommutative deformation of the Kadomtsev-Petviashvili hierarchy
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions
• A generalized frame bundle for certain Fréchet vector bundles and linear connections
• Non-commutative Poisson algebra structures on affine Kac-Moody algebras
• The group of diffeomorphisms of a non-compact manifold is not regular
• Poisson-Lie group of pseudodifferential symbols
• The Kadomtsev-Petviashvili hierarchy with noncommutative time space
• AMBROSE–SINGER THEOREM ON DIFFEOLOGICAL BUNDLES AND COMPLETE INTEGRABILITY OF THE KP EQUATION
• On the way to Frölicher Lie groups
• The Geometry of Infinite-Dimensional Groups
• Microlocal Regularity Theorems for Nonsmooth Pseudodifferential Operators and Applications to Nonlinear Problems
• Jets in differential spaces
• Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable?
• Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
• Algebras whose groups of units are Lie groups
• Pseudo-Differential Operators with Coefficients in Sobolev Spaces
• HOMOGENEOUS SPACES OF INFINITE-DIMENSIONAL LIE ALGEBRAS AND CHARACTERISTIC CLASSES OF FOLIATIONS
• On tangent cones of Frölicher spaces
• Tangent spaces and tangent bundles for diffeological spaces

This page was built for publication: Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups