Results 181 to 190 of about 1,134 (216)

Darboux transformations for Lamé potentials

Czechoslovak Journal of Physics, 2000
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Negro, Javier, Nieto, Luis M., Fernndez C., David J.   +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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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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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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On multidimensional Darboux transformations

Inverse Problems, 1998
Summary: In contrast to known results on one-dimensional Darboux transformations, results on multidimensional Darboux transformations do not seem convenient for disentangling the sets of solutions in global inverse problems. In the present paper, first, we give a broad generalization of vectorial Darboux transformations and a more limited ...
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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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Darboux Transformation of the Nonstationary Dirac Equation

Russian Physics Journal, 2005
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Pecheritsyn, A. A., Pozdeeva, E. O., Samsonov, B. F.   +2 more
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On the existence of Darboux transformations for banded matrices

Applied Mathematics and Computation, 2015
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Dolores Barrios Rolanía, Daniel Manrique   +1 more
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Bäcklund Transformations and Darboux Transformations

1995
In 1883, the German geometer A. V. Backlund found an interesting property of the sine-Gordon equation in studying surfaces of constant negative curvature.[2]
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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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