A package to work with linear partial differential operators

DOI10.1134/S0361768813040063zbMath1311.65180MaRDI QIDQ2017760

Ekaterina Shemyakova

Publication date: 23 March 2015

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

zbMATH Keywords

Darboux transformationsgauge invariantlinear partial differential operatorsmodificationdeterminationLaplace transformation methodcomputer algebra system MAPLEoperator creationoperator pairpackage LPDOsymbolic coefficients

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transform methods (e.g., integral transforms) applied to PDEs (35A22) General theory of partial differential operators (47F05) Packaged methods for numerical algorithms (65Y15)

Related Items (2)

An algorithm for constructing Darboux transformations of type I for third-order hyperbolic operators of two variables ⋮ Invertible Darboux transformations of type I

Uses Software

• Maple
• LPDO

Cites Work

• Moving coframes. II: Regularization and theoretical foundations
• Algebraic-geometric \(n\)-orthogonal curvilinear coordinate systems and solutions of the associativity equations
• On Laplace and Dini transformations for multidimensional equations with a decomposable principal symbol
• On the Invariant Properties of Hyperbolic Bivariate Third-Order Linear Partial Differential Operators
• Invariant Properties of Third-Order Non-hyperbolic Linear Partial Differential Operators
• Proof of the Completeness of Darboux Wronskian Formulae for Order Two
• Moving frames for laplace invariants
• Invariants for Darboux Transformations of Arbitrary Order for $$\mathcal{D}_x\mathcal{D}_y+a\mathcal{D}_x+b\mathcal{D}_y+c$$
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