Higher dimensional Painlevé integrable models from the Kadomtsev–Petviashvili equation

DOI10.1063/1.532576zbMath0927.37047OpenAlexW2044535606MaRDI QIDQ4701489

Jian-Jun Xu, Sen-yue Lou

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532576

zbMATH Keywords

singular manifoldconformal invariancePainlevé analysisKadomtsev-Petviashvili equationhigher dimensional modified Korteweg-de Vries equationsLax integrable models

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) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

Related Items (6)

Solving (3+1)-dimensional non-linear Schrödinger equation by means of (3+1)-dimensional Painlevé integrable model ⋮ Solitary wave solutions for a general Boussinesq type fluid model ⋮ A (3+1)‐dimensional Painlevé integrable model obtained by deformation ⋮ Painlevé integrability and complexiton-like solutions of a coupled Higgs model ⋮ Painlevé test for some \((2+1)\)-dimensional nonlinear equations ⋮ On generalized Lax equations of the Lax triple of the BKP and CKP hierarchies

Cites Work

• Search for high dimensional integrable models
• \((3+1)\)-dimensional models with an infinitely dimensional Virasoro type symmetry algebra
• D Branes from Liouville Strings
• Painleve property and pseudopotentials for nonlinear evolution equations
• The constraints of potentials and the finite-dimensional integrable systems
• New similarity reductions of the Boussinesq equation
• The Painlevé property for partial differential equations
• Integrable and solvable systems, and relations among them
• Lie symmetries of Hirota’s bilinear equations
• A nonconfocal generator of involutive systems and three associated soliton hierarchies
• Deformations of the Riccati equation by using Miura-type transformations
• Method for deriving rational solutions of some nonlinear evolution equations
• Conformal invariance and integrable models
• KdV extensions with Painlevé property
• Infinitely many Lax pairs and symmetry constraints of the KP equation
• Similarity solutions of dispersive long‐wave equations in two space dimensions
• Symmetries of a (2+1)-dimensional breaking soliton equation

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