Results 41 to 50 of about 11,974 (188)

DARBOUX TRANSFORMS AND ORTHOGONAL POLYNOMIALS [PDF]

Bulletin of the Korean Mathematical Society, 2002
In [\textit{F. A. Grünbaum} and \textit{L. Haine}, Symmetries and Integrability of Differential Equations, Estérel, 1994, CRM Proc. Lect. Notes 9, 143-154 (1996; Zbl 0865.33008)] the Darboux transform was used to obtain so-called Bochner-Krall orthogonal polynomials which satisfy a higher order (\(>2\)) spectral type differential equation. This Darboux
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D-Modules and Darboux Transformations

Letters in Mathematical Physics, 1998
A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of partial differential operators with rational spectral varieties.
Berest, Yu., Kasman, A.
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Darboux transformation and multi-soliton solutions of Two-Boson hierarchy

, 2010
We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on $SL(2,R)$ within
Ablowitz M. J., ASHOK DAS, Darboux G., Dodd R. K., Drinfeld V. G., Lamb G. L., U. SALEEM   +6 more
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Solutions to the Sine-Gordon Equation: From Darboux Transformations to Wronskian Representations of the k-Negaton-l-Positon-n-Soliton Solutions

Axioms
With a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation as well as the multiple Darboux transformation, which enables the obtainment of compact solutions of this equation ...
Pierre Gaillard
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New Exactly Solvable Isospectral Partners for PT Symmetric Potentials

, 2003
We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to higher states of
Abramowitz M, Anjana Sinha, Bender C M, Bender C M, Lévai G, Matveev V B, Pinaki Roy, Robnik M, Znojil M, Znojil M   +9 more
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Differential Calculi on Associative Algebras and Integrable Systems

, 2020
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from ...
A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Sitarz, C Rogers, D-J Zhang, E Brezin, F Magri, F Magri, G Chavchanidze, G Tondo, J Grifone, J Hietarinta, JT Hartwig, LJ Mason, M Crampin, M Crampin, O Chvartatskyi, P Lorenzoni, P Lorenzoni, VA Marchenko, VK Mel’nikov, Y Kosmann-Schwarzbach   +30 more
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A New Discrete Integrable System Derived from a Generalized Ablowitz-Ladik Hierarchy and Its Darboux Transformation

Discrete Dynamics in Nature and Society, 2012
We find an interesting phenomenon that the discrete system appearing in a reference can be reduced to the old integrable system given by Merola, Ragnisco, and Tu in another reference.
Xianbin Wu, Weiguo Rui, Xiaochun Hong
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Characters of Explicit Solutions for a Semidiscrete Integrable Coupled Equation

Advances in Mathematical Physics, 2021
A semidiscrete integrable coupled system is obtained by embedding a free function into the discrete zero-curvature equation. Then, explicit solutions of the first two nontrivial equations in this system are derived directly by the Darboux transformation ...
Qiulan Zhao, Qianqian Yang, Xiangwen Qu
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Generalized Darboux transformations for the KP equation with self-consistent sources

, 2004
The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS.
Ablowitz M J, Cheng Y, Cheng Y, Date E, Deng S F, Dickey L A, Dickey L A, Doktorov E V, Leon J, Matveev V B, Mel'nikov V K, Mel'nikov V K, Mel'nikov V K, Mel'nikov V K, Mel'nikov V K, Oevel W, Ohta Y, Sidorenko J, Ting Xiao, Ye S, Yunbo Zeng, Zeng Y B, Zeng Y B   +22 more
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Darboux transformations of coherent states of the time-dependent singular oscillator [PDF]

, 2004
Darboux transformation of both Barut-Girardello and Perelomov coherent states for the time-dependent singular oscillator is studied. In both cases the measure that realizes the resolution of the identity operator in terms of coherent states is found and ...
Agraval G S, Akhieezer N I, Bagrov V G, Bagrov V G, Bagrov V G, Bagrov V G, Barut A O, Beribe-Lavzier Y, Boris F Samsonov, Chumakov S M, de Matos Filho R L, Dodonov V V, Dodonov V V, Erdelyi A, Erdelyi A, Fernandez C D J, Fernandez C D J, Gazeau J P K, Glasser M L, Haroch S, Hartmann A, Klauder J R, Malkin I A, Matveev V, Miller W, Nieto M, Paul W, Perelomov A M, Prudnikov A P, Rosas-Ortiz O J, Samsonov B F, Samsonov B F, Samsonov B F, Samsonov B F, Schrödinger E, Spiridonov V   +35 more
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