On the nature of the Gardner transformation

DOI10.1063/1.524928zbMath0473.35068OpenAlexW2033784697MaRDI QIDQ3927595

Boris A. Kupershmidt

Publication date: 1981

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

Full work available at URL: http://hdl.handle.net/2027.42/69433

zbMATH Keywords

conservation lawsKorteweg-de Vries equationGardner transformationone-parameter family of integrable equations

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

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Korteweg-de Vries surfaces and Bäcklund curves, Evolution equations and \(\text{sl}(2, \mathbb R)\)-valued Bäcklund forms, Time-delay and reality conditions for complex solitons, On algebraic models of dynamical systems, Supersymmetric extension of the Korteweg–de Vries equation, A deformation of the general zero-curvature equations associated to simple Lie algebras, Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations, Integrable nonlocal Hirota equations, Singular symmetries of integrable curves and surfaces, Boussinesq hierarchy and bi-Hamiltonian geometry, On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

Cites Work

• Algebraic aspects of nonlinear differential equations
• Commuting flows and conservation laws for Lax equations
• The Korteweg–deVries Equation: A Survey of Results
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Some Properties of Long Nonlinear Waves