Results 31 to 40 of about 11,987 (207)
Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS
Nuclear Physics B, 2017 We consider the discrete and continuous vector non-linear Schrödinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the
Panagiota Adamopoulou +2 more
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Discrete Dynamics in Nature and Society, 2018 An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established.
Xi-Xiang Xu, Meng Xu
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The Solutions of the NLS Equations with Self-Consistent Sources [PDF]
, 2004 We construct the generalized Darboux transformation with arbitrary functions in time $t$ for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a non-auto-B\"{a ...
Barran S +20 more
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New Darboux Transformation for Hirota-Satsuma coupled KdV System
, 2002 A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlev\'{e} analysis and reduction of a binary Darboux transformation.
Hu, Heng Chun, Liu, Q. P.
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On Darboux transformation of the supersymmetric sine-Gordon equation [PDF]
, 2006 Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super B\"{a}cklund transformation and is further used ...
Aratyn H +7 more
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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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The Bianchi-Darboux transform of L-isothermic surfaces
, 2000 We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation.
Musso, E., Nicolodi, L.
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Solution of High-Order Nonlinear Integrable Systems Using Darboux Transformation
Axioms, 2023 The 4×4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure.
Xinhui Wu, Jiawei Hu, Ning Zhang
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Supersymmetric KdV equation: Darboux transformation and discrete systems
, 2013 For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}.
Levi, D., Liu, Q. P., Xue, Ling-Ling
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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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