Nonlinear evolution equations: Bäcklund transformations and Bäcklund charts

DOI10.1007/s10440-012-9729-8zbMath1280.37055OpenAlexW2079104320MaRDI QIDQ1928089

Sandra Carillo

Publication date: 2 January 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-012-9729-8

zbMATH Keywords

Bäcklund transformationsBäcklund charthierarchies of non-commutative evolution equationsnon-commutative evolution equations

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) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (7)

The non-commutative Korteweg-de Vries hierarchy and combinatorial Pöppe algebra ⋮ Bäcklund transformations and non-abelian nonlinear evolution equations: a novel Bäcklund chart ⋮ The algebraic structure of the non-commutative nonlinear Schrödinger and modified Korteweg-de Vries hierarchy ⋮ Recursion operators admitted by non-abelian Burgers equations: some remarks ⋮ KdV-type equations linked via Bäcklund transformations: remarks and perspectives ⋮ Abelian versus non-abelian Bäcklund charts: some remarks ⋮ Matrix Solitons Solutions of the Modified Korteweg–de Vries Equation

Cites Work

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• Infiltration in soils with prescribed boundary concentration
• A new approach to the quantum KdV.
• Soliton structure versus singularity analysis: Third-order completely integrable nonlinear differential equations in \(1+1\)-dimensions
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Bäcklund transformations and their applications
• On Harry-Dym equation and its solution
• Integrable evolution equations on associative algebras
• Squared eigenfunction symmetries for soliton equations. I
• Squared eigenfunction symmetries for soliton equations. II
• A direct method for studying soliton equations
• The action-angle transformation for soliton equations
• The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems
• On the Recursion Operator for the Noncommutative Burgers Hierarchy
• 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
• EXPLICIT SOLUTION FORMULAS FOR THE MATRIX-KP
• Application of hereditary symmetries to nonlinear evolution equations
• Bäcklund transformations for hereditary symmetries
• Explicit solutions for the Harry Dym equation
• A simple model of the integrable Hamiltonian equation
• Nonlinear equations in soliton physics and operator ideals
• On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchies
• Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions
• On realizations of solutions of the KdV equation by determinants on operator ideals
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics
• Nonlinear boundary value problems in science and engineering

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