Results 31 to 40 of about 9,686 (209)
Non-polynomial extensions of solvable potentials a la Abraham-Moses [PDF]
, 2013 Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics.
Darboux G., Ryu Sasaki, Satoru Odake
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Solitons and the generalized Cole-Hopf substitutions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 This paper examines the relationship between the method of the inverse problem and the method of generalized Cole-Hopf substitutions. The relationship between these methods is established by comparing the method of Darboux transformations and the method ...
V. M. Zhuravlev, A. N. Byzykchi
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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. +6 more
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Darboux Transformation for the Hirota Equation
Zurnal matematiceskoj fiziki, analiza, geometrii, 2022 The Hirota equation is an integrable higher order nonlinear Schrödinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions.
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Periodic discrete Darboux transforms
Differential Geometry and its Applications, 2023 We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence.
Joseph Cho, Katrin Leschke, Yuta Ogata
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Acta et Commentationes: Ştiinţe Exacte şi ale Naturii, 2019 The Lotka-Volterra cubicdifferential systems with (1:-2)-singularity possessing invariant straight lines of two direction and total multiplicity six are classified.
Silvia TURUTA
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, 2003 With this paper we begin an investigation of difference schemes that possess Darboux transformations and can be regarded as natural discretizations of elliptic partial differential equations.
A. Doliwa +31 more
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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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On Darboux transformations for the derivative nonlinear Schr\"odinger equation [PDF]
, 2014 We consider Darboux transformations for the derivative nonlinear Schr\"odinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented and proved.
Nimmo, Jonathan J. C., Yilmaz, Halis
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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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