On the structure and properties of the singularity manifold equations of the KP hierarchy

DOI10.1063/1.529505zbMath0734.58024OpenAlexW1971696825MaRDI QIDQ3361584

B. G. Konopelchenko, Walter Strampp

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1063/1.529505

zbMATH Keywords

inverse scattering transformBäcklund transformationsPainlevé analysisKadomtsev-Petviashvili 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) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items

A KdV equation in 2+1 dimensions: Painlevé analysis, solutions and similarity reductions, Some remarks on symmetries, dressing, and virasoro action, Symmetries, sato theory, and tau functions, Painlevé Analysis and Singular Manifold Method for a (2 + 1) Dimensional Non-Linear Schrödinger Equation, A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions, Darboux transformation and solutions for an equation in 2+1 dimensions, Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations, \(D\) bar dressing and Sato theory

Cites Work

• Solitons and infinite dimensional Lie algebras
• General \(N\)th-order differential spectral problem: general structure of the integrable equations, nonuniqueness of recursion operator and gauge invariance
• Soliton structure versus singularity analysis: Third-order completely integrable nonlinear differential equations in \(1+1\)-dimensions
• Recursion operators and bi-Hamiltonian structures in multidimensions. II
• On the formulation of the Painleve test as a criterion of complete integrability of partial differential equations
• The sine-Gordon equations: Complete and partial integrability
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• On generalisation of the Backlund-Calogero transformations for integrable equations
• Conserved quantities and symmetries of KP hierarchy
• The Painlevé property for partial differential equations
• On classes of integrable systems and the Painlevé property
• The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
• The Painlevé Property and Hirota's Method
• Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations
• Painleve analysis of the non-linear Schrodinger family of equations
• Periodic fixed points of Bäcklund transformations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• On the Painlevé property of nonlinear field equations in 2+1 dimensions: The Davey–Stewartson system
• The Recursion Operator of the Kadomtsev‐Petviashvili Equation and the Squared Eigenfunctions of the Schrödinger Operator