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Discrete Solitons and Bäcklund Transformation for the Coupled Ablowitz–Ladik Equations

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Published/Copyright: September 26, 2017
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 72 Issue 10

Abstract

Under investigation in this paper are the coupled Ablowitz–Ladik equations, which are linked to the optical fibres, waveguide arrays, and optical lattices. Binary Bell polynomials are applied to construct the bilinear forms and bilinear Bäcklund transformation. Bright/dark one- and two-soliton solutions are also obtained. Asymptotic analysis indicates that the interactions between the bright/dark two solitons are elastic. Amplitudes and velocities of the bright solitons increase as the value of the lattice spacing increases. Increasing value of the lattice spacing can lead to the increase of both the bright solitons’ amplitudes and velocities, and the decrease of the velocities of the dark solitons. The lattice spacing parameter has no effect on the amplitudes of the dark solitons. Overtaking interaction between the unidirectional bright two solitons and a bound state of the two equal-velocity solitons is presented. Overtaking interaction between the unidirectional dark two solitons and the two parallel dark solitons is also plotted.

Keywords: Bäcklund Transformation; Coupled Ablowitz–Ladik Equations; Discrete Bright/Dark Solitons; Soliton Interaction

Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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Received: 2017-6-7
Accepted: 2017-8-23
Published Online: 2017-9-26
Published in Print: 2017-9-26

©2017 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Dyons and Certain Symmetries in Maxwell’s Equations
  3. Shear Alfvén Wave with Quantum Exchange-Correlation Effects in Plasmas
  4. Homotopy Perturbation Method for Creeping Flow of Non-Newtonian Power-Law Nanofluid in a Nonuniform Inclined Channel with Peristalsis
  5. Asymptotic Analysis of a Nonlinear Problem on Domain Boundaries in Convection Patterns by Homotopy Renormalization Method
  6. The Exchange-Correlation Field Effect over the Magnetoacoustic-Gravitational Instability in Plasmas
  7. Structural, Spectroscopic, and Energetic Parameters of Diatomic Molecules Having Astrophysical Importance
  8. The Homotopy Perturbation Method for Accurate Orbits of the Planets in the Solar System: The Elliptical Kepler Equation
  9. Electron-Nuclear Dynamics on Amplitude and Frequency Modulation of Molecular High-Order Harmonic Generation from H2+ and its Isotopes
  10. Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation
  11. Discrete Solitons and Bäcklund Transformation for the Coupled Ablowitz–Ladik Equations
  12. Rapid Communication
  13. Nonclassical t-Dependent Energy Integral of q″+aq′+b(t)q+c(t)qn=0
https://doi.org/10.1515/zna-2017-0196
Keywords for this article
Bäcklund Transformation; Coupled Ablowitz–Ladik Equations; Discrete Bright/Dark Solitons; Soliton Interaction

Articles in the same Issue

  1. Frontmatter
  2. Dyons and Certain Symmetries in Maxwell’s Equations
  3. Shear Alfvén Wave with Quantum Exchange-Correlation Effects in Plasmas
  4. Homotopy Perturbation Method for Creeping Flow of Non-Newtonian Power-Law Nanofluid in a Nonuniform Inclined Channel with Peristalsis
  5. Asymptotic Analysis of a Nonlinear Problem on Domain Boundaries in Convection Patterns by Homotopy Renormalization Method
  6. The Exchange-Correlation Field Effect over the Magnetoacoustic-Gravitational Instability in Plasmas
  7. Structural, Spectroscopic, and Energetic Parameters of Diatomic Molecules Having Astrophysical Importance
  8. The Homotopy Perturbation Method for Accurate Orbits of the Planets in the Solar System: The Elliptical Kepler Equation
  9. Electron-Nuclear Dynamics on Amplitude and Frequency Modulation of Molecular High-Order Harmonic Generation from H2+ and its Isotopes
  10. Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation
  11. Discrete Solitons and Bäcklund Transformation for the Coupled Ablowitz–Ladik Equations
  12. Rapid Communication
  13. Nonclassical t-Dependent Energy Integral of q″+aq′+b(t)q+c(t)qn=0
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