Results 11 to 20 of about 1,595,275 (210)

A grassmannian version of the darboux transformation [PDF]

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
openaire   +2 more sources

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
openaire   +4 more sources

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
openaire   +5 more sources

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
doaj   +5 more sources

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, Mañas Baena, Manuel Enrique   +1 more
openaire   +5 more sources

The Darboux transformation of some Manakov systems [PDF]

Applied Mathematics Letters, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wright, O.C
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Solution of High-Order Nonlinear Integrable Systems Using Darboux Transformation

Axioms, 2023
The 4×4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure.
Xinhui Wu, Jiawei Hu, Ning Zhang
doaj   +2 more sources

Darboux transformation of symmetric Jacobi matrices and Toda lattices [PDF]

Frontiers in Applied Mathematics and Statistics
Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
doaj   +4 more sources

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, Chara Pantazi   +1 more
doaj   +7 more sources