\(X\)- and \(Y\)-invariants of partial differential operators in the plane

DOI10.1134/S0361768811020095zbMath1255.35020arXiv1010.3418MaRDI QIDQ764003

E. S. Shemyakova

Publication date: 12 March 2012

Published in: Programming and Computer Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3418

zbMATH Keywords

gauge transformationsDarboux theoremsdifferential substitutionssymbolic solution of differential equationstransformation of hyperbolic operators

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (1)

Laplace transformations as the only degenerate Darboux transformations of first order

Cites Work

• Unnamed Item
• Integrals, solutions, and existence problems for Laplace transformations of linear hyperbolic systems
• Differential transformations of parabolic second-order operators in the plane
• The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane
• On Laplace and Dini transformations for multidimensional equations with a decomposable principal symbol
• Exactly integrable hyperbolic equations of Liouville type
• On the singularities of potentials of exactly soluble Schrödinger equations and on Hadamard's problem
• Exactly soluble periodic two-dimensional Schrödinger operators

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