Results 211 to 220 of about 2,294,985 (248)

12. Darboux transforms

2002
12.1 Ricati equations 12.2 Constant mean curvature surfaces in \({\mathbb{R}}^3\) 12.3 Darboux transforms of Willmore ...
Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall   +4 more
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Two-sided Darboux transformations

Theoretical and Mathematical Physics, 2012
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Shabat, A. B., Élkanova, Z. S., Urusova, A. B.   +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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Higher dimensional Darboux transformations

Journal of Mathematical Analysis and Applications, 2018
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Hovhannisyan, Gro, Ruff, Oliver, Zhang, Zijing   +2 more
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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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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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Higher Rank Darboux Transformations

1994
The Darboux transformation has been discovered several times in history (cf. references in [EK] and in [G3]): the reason for this is its deep geometric significance. In this note we explore some geometric aspects of the transformation and their relevance to the difficult problems of describing explicitly higher-rank commutative algebras of ordinary ...
Geoff Latham, Emma Previato
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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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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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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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