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Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions

  • Guixian Wang EMAIL logo , Xiu-Bin Wang ORCID logo , Bo Han EMAIL logo and Qi Xue
Published/Copyright: February 10, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 4

Abstract

In this paper, the inverse scattering approach is applied to the Kundu-Eckhaus equation with two cases of zero boundary condition (ZBC) and nonzero boundary conditions (NZBCs) at infinity. Firstly, we obtain the exact formulae of soliton solutions of three cases of N simple poles, one higher-order pole and multiple higher-order poles via the associated Riemann-Hilbert problem (RHP). Moreover, given the initial data that allow for the presence of discrete spectrum, the higher-order rogue waves of the equation are presented. For the case of NZBCs, we can construct the infinite order rogue waves through developing a suitable RHP. Finally, by choosing different parameters, we aim to show some prominent characteristics of this solution and express them graphically in detail. Our results should be helpful to further explore and enrich the related nonlinear wave phenomena.

Keywords: inverse scattering method; Riemann-Hilbert problems; rogue waves; solitons; The Kundu-Eckhaus equation
PACS: 02.30.Ik; 04.20.Jb; 05.45.Yv
Corresponding authors: Guixian WangandBo Han, Department of Mathematics, Harbin Institute of Technology, Harbin150001, People’s Republic of China, E-mail: (G. Wang), (B. Han)

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11871180

Acknowledgments

We express our sincere thanks to the editor and reviewers for their valuable comments.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work is supported by the National Natural Science Foundation of China under Grant No. 11871180.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-11-22
Accepted: 2021-01-17
Published Online: 2021-02-10
Published in Print: 2021-04-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2020-0327
Keywords for this article
inverse scattering method; Riemann-Hilbert problems; rogue waves; solitons; The Kundu-Eckhaus equation

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Rapid Communication
  4. All waves have a zero tunneling time
  5. Atomic, Molecular & Chemical Physics
  6. Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals
  7. Dynamical Systems & Nonlinear Phenomena
  8. Dynamics of liquid drop on a vibrating micro-perforated plate
  9. Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions
  10. Evolution of nonlinear stationary formations in a quantum plasma at finite temperature
  11. Solid State Physics & Materials Science
  12. Effect of ZnO nanoparticles on optical textures and image analysis properties of 7O.O5 liquid crystalline compound
  13. First-principles study on band gaps and transport properties of van der Waals WSe2/WTe2 heterostructure
  14. Dirac cones for graph models of multilayer AA-stacked graphene sheets
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