Results 21 to 30 of about 11,987 (207)
Exceptional orthogonal polynomials and the Darboux transformation [PDF]
, 2010 We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation.
Atkinson F V +21 more
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N-Fold Darboux transformation of the discrete Ragnisco–Tu system
Advances in Difference Equations, 2018 In this paper, based on gauge transformation of Lax pairs, we construct an N-fold Darboux transformation for the discrete Ragnisco–Tu equation which is a typical member in the Ragnisco–Tu hierarchy.
Ning Zhang, Tiecheng Xia, QiuYan Jin
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The Darboux system: Finite-rank constraints and Darboux transformations [PDF]
Journal of Mathematical Physics, 1997 The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, which can be understood as a vectorial Darboux transformation of the exponential background.
Guil Guerrero, Francisco José +1 more
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Miura and Darboux transformations in the SUSY KP hierarchies
Nuclear Physics B, 2022 The Miura links between the KP and modified KP hierarchies are extended to the SUSY KP (SKP) and SUSY modified KP hierarchies (SmKP) of Manin Radul and Jacobian types.
Huizhan Chen, Jipeng Cheng, Zhiwei Wu
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Darboux transformation: new identities [PDF]
Physica Scripta, 2019 This letter reports some new identities for multisoliton potentials that are based on the explicit representation provided by the Darboux matrix. These identities can be used to compute the complex gradient of the energy content of the tail of the profile with respect to the discrete eigenvalues and the norming constants. The associated derivatives are
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Rational Solutions of a Weakly Coupled Nonlocal Nonlinear Schrödinger Equation
Advances in Mathematical Physics, 2018 In this article, we investigate an integrable weakly coupled nonlocal nonlinear Schrödinger (WCNNLS) equation including its Lax pair. Afterwards, Darboux transformation (DT) of the weakly coupled nonlocal NLS equation is constructed, and then the ...
Huijuan Zhou +2 more
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Acta Polytechnica, 2023 We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates.
Axel Schulze-Halberg
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Generalized Algebraic Bargmann–Darboux Transformations [PDF]
International Journal of Modern Physics A, 1997 Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schrödinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed. The suggested generalized transformations turn into the Bargmann and Darboux transformations for both fixed and variable values of energy and an
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Mathematics, 2021 In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given.
Yu-Shan Bai, Peng-Xiang Su, Wen-Xiu Ma
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Distortion of a Phase Space Under the Darboux Transformation [PDF]
, 1997 The Darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states.
Samsonov, Boris F.
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