Results 11 to 20 of about 1,134 (216)
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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A generalized method for the Darboux transformation [PDF]
Journal of Mathematical Physics, 2022 A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of discrete eigenvalues are added to or removed from the spectrum.
Tuncay Aktosun, Mehmet Unlu
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Darboux Transformation for the Hirota Equation [PDF]
Zurnal matematiceskoj fiziki, analiza, geometrii, 2022 The Hirota equation is an integrable higher order nonlinear Schrödinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions.
Yılmaz, Halis, Yilmaz, Halis
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The multidimensional Darboux transformation [PDF]
Journal of Geometry and Physics, 1998 plain TeX, 29 pages.
González López, Artemio, Kamran, Niky
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A grassmannian version of the darboux transformation
Bulletin des Sciences Mathématiques, 1999 In soliton theory, a Darboux transformation (DT) refers to the following process: First factorize a given second order operator \(L=(d/dx)^2-q\) as a product of two first order operators. Then, swap the order of these operators to obtain a new operator \(\widetilde{L}=(d/dx)^2-\widetilde{q}\).
Fastré, Jean, Jean Fastré
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N-Fold Darboux transformation of the discrete Ragnisco–Tu system
Advances in Difference Equations, 2018 In this paper, based on gauge transformation of Lax pairs, we construct an N-fold Darboux transformation for the discrete Ragnisco–Tu equation which is a typical member in the Ragnisco–Tu hierarchy.
Ning Zhang, Tiecheng Xia, QiuYan Jin
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Partial Differential Equations in Applied Mathematics, 2023 An one-fold Darboux transformation for the Lotka–Volterra lattice system is first established using a proper gauge transformation matrix. Then, as a result of the N times one-fold Darboux transformation, the corresponding N-fold Darboux transformation of
Rong-Wu Lu, Xi-Xiang Xu
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The Darboux system: Finite-rank constraints and Darboux transformations [PDF]
Journal of Mathematical Physics, 1997 The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, which can be understood as a vectorial Darboux transformation of the exponential background.
Guil Guerrero, Francisco José +1 more
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Results in Physics, 2016 We demonstrate that the Darboux transformation in the paper “Soliton solutions by Darboux transformation and some reductions for a new Hamiltonian lattice hierarchy” [Phys. Scr.
Xi-Xiang Xu
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