On the theory of Laplace-Darboux transformations

DOI10.1007/BF02069791zbMath0855.35004MaRDI QIDQ1920616

A. B. Shabat

Publication date: 12 January 1997

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Laplace-Darboux theorylinear-fractional transformation

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Linear higher-order PDEs (35G05)

Related Items (13)

Solutions of two-dimensional Schrödinger-type equations in a magnetic field ⋮ Differential operators on the superline, Berezinians, and Darboux transformations ⋮ Semidiscrete Toda lattices ⋮ Darboux system and separation of variables in the Goursat problem for a third order equation in \(\mathbb{R}^3\) ⋮ Classification of multidimensional Darboux transformations: first order and continued type ⋮ The dressing method and separation of variables: the two-dimensional case ⋮ Darboux transformations for factorable Laplace operators ⋮ Factorization of Darboux-Laplace transformations for discrete hyperbolic operators ⋮ Darboux integrability of discrete two-dimensional Toda lattices ⋮ Classification of Darboux transformations for operators of the form \(\partial_x\partial_y+a\partial_x+b\partial_y+c\) ⋮ Some generalizations of the two-dimensional Toda chain and sinh-Gordon equations ⋮ Conjugate chains of discrete symmetries in \(1+2\) nonlinear equations ⋮ A hierarchy of generalized invariants for linear partial differential operators

Cites Work

• A correction to the paper ``Hypergeometric functions and toric varieties

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