Intertwining Laplace Transformations of Linear Partial Differential Equations

DOI10.1007/978-3-642-54479-8_4zbMath1375.35010arXiv1306.1113OpenAlexW1946898927MaRDI QIDQ5403091

Elena I. Ganzha

Publication date: 25 March 2014

Published in: Algebraic and Algorithmic Aspects of Differential and Integral Operators (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.1113

zbMATH Keywords

Laplace transformdifferential transformationintegration of linear partial differential equations

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Laplace transform (44A10)

Related Items

An algorithm for constructing Darboux transformations of type I for third-order hyperbolic operators of two variables ⋮ Twisted Laplace maps ⋮ Classification of multidimensional Darboux transformations: first order and continued type ⋮ Laplace invariants of differential operators ⋮ Classification of Darboux transformations for operators of the form \(\partial_x\partial_y+a\partial_x+b\partial_y+c\)

Cites Work

• Exact solutions of hyperbolic systems of kinetic equations. Application to Verhulst model with random perturbation
• Differential transformations of parabolic second-order operators in the plane
• The Riquier-Janet theory and its application to nonlinear evolution equations
• Laplace transformations as the only degenerate Darboux transformations of first order
• On Laplace and Dini transformations for multidimensional equations with a decomposable principal symbol
• Theory of non-commutative polynomials
• A \(\mathbf Z^2\times\mathbf R^3\) Toda system
• The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications
• 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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