On the Recursion Operator for the Noncommutative Burgers Hierarchy

DOI10.1142/S1402925112500039zbMath1279.37043MaRDI QIDQ2883213

Sandra Carillo, Cornelia Schiebold

Publication date: 11 May 2012

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

zbMATH Keywords

Burgers equationrecursion operatorsBäcklund transformationsnoncommutativityhereditariness

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) Applications of operator theory to differential and integral equations (47N20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (8)

Bäcklund transformations and non-abelian nonlinear evolution equations: a novel Bäcklund chart ⋮ Nonlinear evolution equations: Bäcklund transformations and Bäcklund charts ⋮ A novel noncommutative KdV-type equation, its recursion operator, and solitons ⋮ Recursion operators admitted by non-abelian Burgers equations: some remarks ⋮ KdV-type equations linked via Bäcklund transformations: remarks and perspectives ⋮ The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation ⋮ Abelian versus non-abelian Bäcklund charts: some remarks ⋮ Matrix Solitons Solutions of the Modified Korteweg–de Vries Equation

Cites Work

• Computer-algebra methods for investigation of hereditary operators of higher order soliton equations
• Integrable evolution equations on associative algebras
• Classification of Integrable One-Component Systems on Associative Algebras
• Structural properties of the noncommutative KdV recursion operator
• Noncommutative Korteweg–de Vries and modified Korteweg–de Vries hierarchies via recursion methods
• On A Group Of Automorphisms Of The Noncommutative Burgers Hierarchy
• The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links
• On Non-Commutative Integrable Burgers Equations
• Application of hereditary symmetries to nonlinear evolution equations
• Bäcklund transformations for hereditary symmetries
• Evolution equations possessing infinitely many symmetries
• On construction of recursion operators from Lax representation
• Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions

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