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   Articles with "darboux transformation" as a keyword



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On the Darboux transformation of a generalized inhomogeneous higher-order nonlinear Schrödinger equation

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recommendations! Published in 2017 at "Nonlinear Dynamics"

DOI: 10.1007/s11071-016-3026-4

Abstract: Recently, a paper about the Nth-order rogue waves for an inhomogeneous higher-order nonlinear Schrödinger equation using the generalized Darboux transformation is published. Song et al. (Nonlinear Dyn 82(1):489–500. doi:10.1007/s11071-015-2170-6, 2015). However, the inhomogeneous equation which… read more here.

Keywords: higher order; equation; inhomogeneous higher; darboux transformation ... See more keywords
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Darboux transformation and nonautonomous solitons for a generalized inhomogeneous Hirota equation

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recommendations! Published in 2017 at "Indian Journal of Physics"

DOI: 10.1007/s12648-016-0903-0

Abstract: In this paper, a generalized inhomogeneous Hirota equation with spatial inhomogeneity and nonlocal nonlinearity is investigated in detail. Firstly, the Darboux transformation is constructed based on corresponding nonisospectral linear eigenvalue problem. This transformation has an… read more here.

Keywords: generalized inhomogeneous; hirota equation; transformation; darboux transformation ... See more keywords
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A new lattice hierarchy: Hamiltonian structures, symplectic map and N-fold Darboux transformation

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recommendations! Published in 2019 at "Applied Mathematical Modelling"

DOI: 10.1016/j.apm.2018.10.030

Abstract: Abstract A new lattice hierarchy is constructed from a discrete matrix spectral problem. By the Tu scheme technique, the associated Hamiltonian structures and infinitely many conservation laws of this hierarchy are derived. Then a symplectic… read more here.

Keywords: symplectic map; lattice hierarchy; new lattice; darboux transformation ... See more keywords
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Dynamical behaviour of rogue wave solutions in a multi-component AB system

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recommendations! Published in 2019 at "Wave Motion"

DOI: 10.1016/j.wavemoti.2019.02.006

Abstract: Abstract With the aid of a 3 × 3 matrix spectral problem, we propose a multi-component AB system to describe self-induced transparency phenomenon. Based on the gauge transformation between the spectral problems, a one-fold Darboux transformation of… read more here.

Keywords: darboux transformation; system; component system; multi component ... See more keywords
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Darboux transformation and soliton solutions of a nonlocal Hirota equation

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recommendations! Published in 2021 at "Chinese Physics B"

DOI: 10.1088/1674-1056/ac11e9

Abstract: Starting from local coupled Hirota equations, we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as AKNS scattering problem. The Lax integrability of the nonlocal Hirota equation is guaranteed also… read more here.

Keywords: darboux transformation; equation; hirota equation; nonlocal hirota ... See more keywords
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Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation

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recommendations! Published in 2017 at "Modern Physics Letters B"

DOI: 10.1142/s0217984917502761

Abstract: By modifying the scheme for an isospectral problem, the non-isospectral Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy is constructed via allowing the time varying spectrum. In this paper, we consider an integrable nonautonomous nonlinear integro-differential Schrodinger equation discussed before… read more here.

Keywords: nonautonomous nonlinear; integro differential; integrable nonautonomous; equation ... See more keywords
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N-fold Darboux transformation and conservation laws of the modified Volterra lattice

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recommendations! Published in 2018 at "Modern Physics Letters B"

DOI: 10.1142/s0217984918504092

Abstract: In this work, we study the modified Volterra lattice. Applying the gauge transformation of the associated [Formula: see text] matrix spectral problems, we establish the N-fold Darboux transformation (DT), and then construct a few explicit… read more here.

Keywords: volterra lattice; fold darboux; modified volterra; darboux transformation ... See more keywords
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Darboux transformation approach for two new coupled nonlinear evolution equations

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recommendations! Published in 2019 at "Modern Physics Letters B"

DOI: 10.1142/s0217984920500049

Abstract: A new coupled Burgers equation and a new coupled KdV equation which are associated with 3 × 3 matrix spectial problem are investigated for complete integrability and covariant property. For integra... read more here.

Keywords: approach two; two new; new coupled; transformation approach ... See more keywords
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A Relativistic Toda Lattice Hierarchy, Discrete Generalized (m, 2N-m)-Fold Darboux Transformation and Diverse Exact Solutions

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recommendations! Published in 2021 at "Symmetry"

DOI: 10.3390/sym13122315

Abstract: This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Firstly, we… read more here.

Keywords: lattice; toda lattice; darboux transformation; exact solutions ... See more keywords