Theory of connections, Cole-Hopf transformations and potentials of second-order partial differential equations

DOI10.3103/S1066369X07090034zbMath1151.58022OpenAlexW2015798284MaRDI QIDQ941290

A. K. Rybnikov

Publication date: 4 September 2008

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x07090034

zbMATH Keywords

potentialCole-Hopf transformationsecond-order partial differential equationBäcklund transformationconnection

Mathematics Subject Classification ID

Jets in global analysis (58A20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Other connections (53B15) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (2)

Connections defining representations of zero curvature and the solitons of sine-Gordon and Korteweg-de Vries equations ⋮ Bäcklund maps and Lie-Bäcklund transformations as differential-geometric structures

Cites Work

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• Local jet bundle formulation of Bäcklund transformations. With applications to non-linear evolution equations
• Differential-geometric structures on manifolds
• Bäcklund transformations and their applications
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

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