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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Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility [PDF]
, 2008 In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients.
A. A. Andrianov +26 more
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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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A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method
Mathematics, 2023 In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation.
Paz Albares, Pilar G. Estévez
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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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Darboux Transformations for Supersymmetric Korteweg - de Vries Equations [PDF]
, 1994 \hspace{.2in}We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu ...
B. A. Kupershmidt +20 more
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Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure [PDF]
Quantum, 2023 In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-
Viktor Zelezny
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B\"acklund-Darboux Transformations and Discretizations of Super KdV Equation [PDF]
, 2014 For a generalized super KdV equation, three Darboux transformations and the corresponding B\"acklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.
Liu, Qing Ping, Xue, Ling-Ling
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MKdV方程和SG方程的可积曲面的构造(Conformation of soliton surfaces of MKdV equation and SG equation)
Zhejiang Daxue xuebao. Lixue ban, 2010 The soliton solutions and the soliton surfaces of Modified Korteweg-de Vries equation (MKdV) and Sine-Gordon (SG) equation by the n-fold Darboux transformation are given out.
ZHANGLing(张玲), DINGNan(丁楠)
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On form-preserving transformations for the time-dependent Schr\"odinger equation [PDF]
, 1999 In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schr\"odinger equation (TDSE).
Artemio González-López +4 more
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