Bäcklund transformations and zero-curvature representations of systems of partial differential equations

DOI10.1063/1.530517zbMath0813.58062arXivhep-th/9405064OpenAlexW2061200549MaRDI QIDQ4314230

Friedemann Brandt

Publication date: 11 December 1994

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

Full work available at URL: https://arxiv.org/abs/hep-th/9405064

zbMATH Keywords

gauge transformationsBäcklund transformationspartial differential equationszero curvature representation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (1)

Constructing solutions of Hamilton–Jacobi equations for 2D fields with one component by means of Bäcklund transformations

Cites Work

• Lie algebras and equations of Korteweg-de Vries type
• On a geometrical property of the Bäcklund transformation of the sine- Gordon equation
• On the zero-curvature representation of a new integrable system in three dimensions
• Prolongation structures of nonlinear evolution equations
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Zero curvature conditions and conformal covariance
• ZERO CURVATURE CONDITION AND 2D GRAVITY THEORIES
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Integrals of nonlinear equations of evolution and solitary waves

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