Results 11 to 20 of about 275 (183)

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

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   +8 more sources

Soliton Solutions to Sasa–Satsuma-Type Modified Korteweg–De Vries Equations by Binary Darboux Transformations

Mathematics
Sasa–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
exaly   +3 more sources

Higher-order Darboux transformations with foreign auxiliary equations and equivalence with generalized Darboux transformations

Applied Mathematics Letters, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Axel Schulze-Halberg
exaly   +3 more sources

Miura and Darboux transformations in the SUSY KP hierarchies

Nuclear Physics B, 2022
The Miura links between the KP and modified KP hierarchies are extended to the SUSY KP (SKP) and SUSY modified KP hierarchies (SmKP) of Manin Radul and Jacobian types.
Huizhan Chen, Jipeng Cheng, Zhiwei Wu
doaj   +1 more source

Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism

Acta Polytechnica, 2023
We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates.
Axel Schulze-Halberg
doaj   +1 more source

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, Xianguo Geng, Bo Xue, Ruomeng Li   +3 more
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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

Explicit solutions of rational integrable differential-difference equations

Partial Differential Equations in Applied Mathematics, 2022
The rational integrable differential-difference equations are proposed from a different discrete spectral problem. We proved the Liouville integrability of rational integrable differential-difference equations by deriving its bi-Hamiltonian structures ...
Qiulan Zhao, Muhammad Arham Amin
doaj   +1 more source

Nonlinear Schrödinger type tetrahedron maps

Nuclear Physics B, 2020
This paper is concerned with the construction of new solutions in terms of birational maps to the functional tetrahedron equation and parametric tetrahedron equation.
S. Konstantinou-Rizos
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