Results 21 to 30 of about 275 (183)
Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation
Advances in Mathematical Physics, 2021 In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear
Irfan Mahmood, Muhammad Waseem
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Darboux transforms of Dupin surfaces [PDF]
Banach Center Publications, 2002 We present a Mobius invariant construction of the Darboux transformation for isothermic surfaces by the method of moving frames and use it to give a complete classification of the Darboux transforms of Dupin ...
MUSSO, EMILIO, NICOLODI L.
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A unified approach to Darboux transformations [PDF]
Inverse Problems, 2009 We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution.
TUNCAY AKTOSUN +1 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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Elementary Darboux Transformations and Factorization [PDF]
Theoretical and Mathematical Physics, 2005 10 ...
Musso, F., Shabat, A. B.
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A generalized method for the Darboux transformation
Journal of Mathematical Physics, 2022 A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of discrete eigenvalues are added to or removed from the spectrum.
Tuncay Aktosun, Mehmet Unlu
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A Five-Component Generalized mKdV Equation and Its Exact Solutions
Mathematics, 2020 In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations
Bo Xue, Huiling Du, Ruomeng Li
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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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On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
Mathematics, 2019 A vector modified Yajima−Oikawa long-wave−short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and ...
Xianguo Geng, Ruomeng Li
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Advances in Mathematical Physics, 2022 In this letter, we consider a new two-component system. By its reciprocal relation with the first negative flow in the AKNS hierarchy, we construct three Darboux-Bäcklund transformations for the new system and obtain some soliton-like solutions.
Shilong Huang, Hongmin Li
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