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Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation

  • Hai-Qiang Zhang EMAIL logo , Xiao-Li Liu und Li-Li Wen
Veröffentlicht/Copyright: 8. Dezember 2015
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 71 Heft 2

Abstract

In this paper, a (2+1)-dimensional nonlinear Schrödinger (NLS) equation, which is a generalisation of the NLS equation, is under investigation. The classical and generalised N-fold Darboux transformations are constructed in terms of determinant representations. With the non-vanishing background and iterated formula, a family of the analytical solutions of the (2+1)-dimensional NLS equation are systematically generated, including the bright-line solitons, breathers, and rogue waves. The interaction mechanisms between two bright-line solitons and among three bright-line solitons are both elastic. Several patterns for first-, second, and higher-order rogue wave solutions fixed at space are displayed, namely, the fundamental pattern, triangular pattern, and circular pattern. The two-dimensional space structures of first-, second-, and third-order rogue waves fixed at time are also demonstrated.

Keywords: Breather; Darboux transformation; (2+1)-Dimensional Nonlinear Schrödinger Equation; Soliton; Rogue Wave
Corresponding author: Hai-Qiang Zhang, College of Science, University of Shanghai for Science and Technology, PO Box 253, Shanghai 200093, China, E-mail:

Acknowledgments

This work is supported by the Shanghai Leading Academic Discipline Project under Grant No. XTKX2012, by Hujiang Foundation of China under Grant No. B14005, by the Natural Science Foundation of Shanghai under Grant No. 12ZR1446800, Science and Technology Commission of Shanghai municipality, and by the National Natural Science Foundation of China under Grant Nos. 11201302 and 11171220.

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Received: 2015-9-30
Accepted: 2015-11-1
Published Online: 2015-12-8
Published in Print: 2016-2-1

©2016 by De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
  3. The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations
  4. Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials
  5. Rational Solutions for Lattice Potential KdV Equation and Two Semi-discrete Lattice Potential KdV Equations
  6. Structural, Electronic, Magnetic and Optical Properties of Ni,Ti/Al-based Heusler Alloys: A First-Principles Approach
  7. Ab Initio Calculations on the Structural, Mechanical, Electronic, Dynamic, and Optical Properties of Semiconductor Half-Heusler Compound ZrPdSn
  8. Qualitative Behaviour of Generalised Beddington Model
  9. Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models
  10. Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals
  11. Investigation of Thermal Expansion and Physical Properties of Carbon Nanotube Reinforced Nanocrystalline Aluminum Nanocomposite
  12. Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions
  13. Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
https://doi.org/10.1515/zna-2015-0408
Schlagwörter für diesen Artikel
Breather; Darboux transformation; (2+1)-Dimensional Nonlinear Schrödinger Equation; Soliton; Rogue Wave

Artikel in diesem Heft

  1. Frontmatter
  2. Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
  3. The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations
  4. Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials
  5. Rational Solutions for Lattice Potential KdV Equation and Two Semi-discrete Lattice Potential KdV Equations
  6. Structural, Electronic, Magnetic and Optical Properties of Ni,Ti/Al-based Heusler Alloys: A First-Principles Approach
  7. Ab Initio Calculations on the Structural, Mechanical, Electronic, Dynamic, and Optical Properties of Semiconductor Half-Heusler Compound ZrPdSn
  8. Qualitative Behaviour of Generalised Beddington Model
  9. Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models
  10. Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals
  11. Investigation of Thermal Expansion and Physical Properties of Carbon Nanotube Reinforced Nanocrystalline Aluminum Nanocomposite
  12. Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions
  13. Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
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