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Invertible Darboux Transformations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae.
Ekaterina Shemyakova
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Generalized Algebraic Bargmann - Darboux Transformations [PDF]
International Journal of Modern Physics A, 1997 Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schr\"odinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed.
Suzko, A. A.
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Minimal Darboux transformations [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016 We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-
Hertrich-Jeromin, U., Honda, A.
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Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the ''invariance'' of the objects of the ''Darboux theory of integrability''. In particular,
Primitivo B. Acosta-Humánez +1 more
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Noncommutative bispectral Darboux transformations
Transactions of the American Mathematical Society, 2016 We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference operators with ...
Geiger, Joel +2 more
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B\"acklund--Darboux transformations in Sato's Grassmannian [PDF]
, 1996 We define B\"acklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators.
Bakalov, B., Horozov, E., Yakimov, M.
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Symmetries and integrable systems [PDF]
Fundamental ResearchSymmetry plays key roles in modern physics especially in the study of integrable systems because of the existence of infinitely many local and nonlocal generalized symmetries.
Sen-Yue Lou, Bao-Feng Feng
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Darboux Transformations for SUSY Integrable Systems [PDF]
, 1997 Several types of Darboux transformations for supersymmetric integrable systems such as the Manin-Radul KdV, Mathieu KdV and SUSY sine-Gordon equations are considered.
A. Bilal +39 more
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Miura and Darboux transformations in the SUSY KP hierarchies
Nuclear Physics B, 2022 The Miura links between the KP and modified KP hierarchies are extended to the SUSY KP (SKP) and SUSY modified KP hierarchies (SmKP) of Manin Radul and Jacobian types.
Huizhan Chen, Jipeng Cheng, Zhiwei Wu
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Acta Polytechnica, 2023 We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates.
Axel Schulze-Halberg
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