Results 1 to 10 of about 433 (167)
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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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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A modified Suris hierarchy and N-fold Darboux -Bäcklund transformation
Partial Differential Equations in Applied Mathematics, 2022 A modified Suris hierarchy is derived by discrete zero curvature equation. Bi-Hamiltonian structure of the whole hierarchy is established through the discrete trace identity. And we prove that the obtained hierarchy is Liouville integrable.
Ning Zhang, Xi-Xiang Xu
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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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The stability of bright–dark solitons in defocusing coupled nonlinear Schrödinger equation
Partial Differential Equations in Applied Mathematics, 2022 The Darboux transformation is a classical method to generate the solitonic solutions for the integrable equations. In this work, we develop the Darboux transformation to analyze the spectral stability of bright–dark soliton for defocusing coupled ...
Liming Ling, Xuan Sun
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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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Darboux transforms of Dupin surfaces [PDF]
Banach Center Publications, 2002 We present a Mobius invariant construction of the Darboux transformation for isothermic surfaces by the method of moving frames and use it to give a complete classification of the Darboux transforms of Dupin ...
MUSSO E., NICOLODI, Lorenzo
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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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Elementary Darboux Transformations and Factorization [PDF]
Theoretical and Mathematical Physics, 2005 10 ...
Musso, F., Shabat, A. B.
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