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Darboux transformation and explicit solutions for two integrable equations [PDF]

Journal of Mathematical Analysis and Applications, 2011
A new N-fold Darboux transformation for two integrable equations is constructed with the help of a gauge transformation for the spectral problem proposed by Qiao [Z.J. Qiao, Phys. Lett. A 192 (1994) 316–322].
Zhijun Qiao
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Darboux transformations for Lamé potentials

Czechoslovak Journal of Physics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Negro, Javier, Nieto, Luis M., Fernndez C., David J.   +2 more
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On the Darboux Transformation. I

gmj, 1995
Abstract Automorphisms of the family of all Sturm-Liouville equations y″ = qy are investigated. The classical Darboux transformation arises as a particular case of a general result.
openaire   +3 more sources

Darboux transformations for “W-problems”

Physica D: Nonlinear Phenomena, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Steudel, H., Meinel, R.
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The Heun Equation and the Darboux Transformation

Mathematical Notes, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sirota, Yu. N., Smirnov, A. O.
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Generalization of the Darboux transform

Journal of Mathematical Physics, 2001
This article presents a generalization of the standard Darboux transform applied to Sturm–Liouville differential equations. This is achieved with the aid of an ansatz as a particular solution for the Riccati relationship involved, which in turn led us to obtain its generalized Darboux solution that contains, as a particular case, the standard Darboux ...
Morales, J., Peña, J. J., López-Bonilla, J. L.   +2 more
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Darboux Transformation of the Laguerre Operator

Complex Analysis and Operator Theory, 2018
For \(\alpha>-1\), let \(L_n(x,\alpha)\), \(n\) a non-negative integer, denote the classical Laguerre polynomials orthogonal in \(L^2(\mathbb R_+,w_\alpha)\), where \(w_\alpha(x)=x^\alpha \cdot e^{-x}\). For \(\alpha>-1\), the classical Laguerre operator \(L_\alpha\) is defined on \(L^2(\mathbb R_+,w_\alpha)\) by \[ L_\alpha(y):= xy^{\prime\prime ...
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Commutation and Darboux transformation

Pramana, 2015
In this paper we show that the Darboux transformation for a large class of nonlinear evolution equations arises due to factorization and commutation. The factorization and commutation has been pointed out earlier for Schrodinger operator. We show that it extends to a large class of nonlinear differential equations which admit Lax pairs including ...
M V PRABHAKAR, H BHATE
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Bäcklund and Darboux Transformations

2002
This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged ...
C. Rogers, W. K. Schief
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On Darboux and singular Darboux transformations ofG-unitons

Science China Mathematics, 2002
We present a unified method for constructing generalized flag transformations of unitons into a Lie groupG via singular Darboux transformations. These flag transformations provide the possibility to establish some factorizations forG-unitons.
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