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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
doaj   +9 more sources

Formal Diagonalisation of Lax-Darboux Schemes

Моделирование и анализ информационных систем, 2015
We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schro¨dinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral ...
A. V. Mikhailov
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
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Integral transformation and Darboux transformation

, 2009
We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum ...
Takemura, Kouichi
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Darboux transformation with dihedral reduction group [PDF]

Journal of Mathematical Physics, 2014
We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference ...
Alexander V. Mikhailov, Drinfel'd V. G., Georgios Papamikos, Jing Ping Wang, Mikhailov A. V., Mikhailov A. V., Mikhailov A. V., Rogers C., Xenitidis P.   +8 more
core   +6 more sources

Coherent Schwinger Interaction from Darboux Transformation [PDF]

Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques, 2009
The exactly solvable scalar-tensor potential of the four-component Dirac equation has been obtained by the Darboux transformation method. The constructed potential has been interpreted in terms of nucleon-nucleon and Schwinger interactions of neutral ...
A. F. Tulinov, B. F. Samsonov, B. Thaller, C. V. Sukumar, E. O. Pozdeeva, E. O. Pozdeeva, F. Partovi, G. Darboux, I. S. Gradshtein, J. F. Donoghue, J. Lindhard, M. T. Robinson, R. S. Nelson, V. G. Bagrov, V. G. Bagrov, V. I. Vysotskii, V. K. Ignatovich, V. V. Fedorov, V. V. Fedorov, Y. Nogami   +19 more
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Lotka–Volterra lattice system: N-fold Darboux transformation, the corresponding integrable lattice family and bi-Hamiltonian structure

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

The multidimensional Darboux transformation [PDF]

Journal of Geometry and Physics, 1998
A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of ...
González López, Artemio, Kamran, Niky
openaire   +5 more sources