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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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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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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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Noncommutative bispectral Darboux transformations [PDF]
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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MathematicsSasa–Satsuma (SS)-type integrable matrix modified Korteweg–de Vries (mKdV) equations are derived from two group constraints, involving the replacement of the spectral matrix in the Ablowitz–Kaup–Newell–Segur matrix eigenproblems with its matrix transpose
Wen-Xiu Ma
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Darboux transformation and exact solutions for a four-component Fokas–Lenells equation
Results in Physics, 2021 In the present paper, we introduce a 4 × 4 matrix spectral problem and derive a four-component Fokas–Lenells equation. N-fold Darboux transformations for the four-component Fokas–Lenells equation are constructed by using the gauge transformation between ...
Yihao Li +3 more
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Classification of Multidimensional Darboux Transformations: First Order and Continued Type [PDF]
, 2017 We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type.
Hobby, David, Shemyakova, Ekaterina
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Binary Darboux transformation for the Sasa–Satsuma equation [PDF]
, 2015 The Sasa-Satsuma equation is an integrable higher-order nonlinear Schr\"odinger equation. Higher-order and multicomponent generalisations of the nonlinear Schr\"odinger equation are important in various applications, e.g., in optics.
Jonathan J C Nimmo, Halis Yilmaz
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Darboux transformations for differential operators on the superline [PDF]
, 2015 We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of ...
Hill, Sean +2 more
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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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