Burgers and Kadomtsev-Petviashvili hierarchies: a functional representation approach

DOI10.1007/s11232-007-0079-zzbMath1131.35070arXivnlin/0610045OpenAlexW3013917471MaRDI QIDQ2461073

Aristophanes Dimakis, Folkert Mueller-Hoissen

Publication date: 21 November 2007

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0610045

zbMATH Keywords

Cole-Hopf transformationKadomtsev-Petviashvili hierarchyBurgers hierarchyfunctional Riccati equation

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) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (5)

Moyal noncommutative integrability and the Burgers--KdV mapping ⋮ Towards noncommutative integrable systems ⋮ Nonlinear quantum-dynamical system based on the Kadomtsev-Petviashvili II equation ⋮ Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems ⋮ Kadomtsev-Petviashvili II equation: structure of asymptotic soliton webs

Cites Work

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• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• From nonassociativity to solutions of the KP hierarchy
• Solving the KP hierarchy by gauge transformations
• Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows
• Matrix Riccati equations in control and systems theory
• Integrable noncommutative equations on quad-graphs. The consistency approach
• The Hopf-Cole transformation and the KP equation
• Riccati differential equations
• On KP generators and the geometry of the HBDE
• On A Group Of Automorphisms Of The Noncommutative Burgers Hierarchy
• From AKNS to derivative NLS hierarchies via deformations of associative products
• The Painlevé property for partial differential equations
• The Hamiltonian structure of a complex version of the Burgers hierarchy
• AUTOMORPHISMS OF BANACH MANIFOLDS ASSOCIATED WITH THE KP-EQUATION
• The Weiss–Tabor–Carnevale Painlevé test and Burgers’ hierarchy
• Hamiltonian formulation of odd Burgers hierarchy
• Noncommutative Burgers equation
• Darboux transformations and linear parabolic partial differential equations
• Nonlinear interaction of traveling waves of nonintegrable equations
• Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
• Noncommutative differential calculus and lattice gauge theory
• Functional representations of integrable hierarchies
• The partial differential equation u_t + uu_x = μ_xx
• Hopf-Cole transformation to some systems of partial differential equations

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