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Volume 11, Issue 2
Riemann-Hilbert Approach and Soliton Solutions of the Higher-Order Dispersive Nonlinear Schrödinger Equations with Single and Double Poles

Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang & Xiao-Li Wang

DOI: 10.4208/eajam.240920.291120

East Asian J. Appl. Math., 11 (2021), pp. 369-388.

Published online: 2021-02

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  • Abstract

The higher-order dispersive nonlinear Schrödinger equation with the zero boundary conditions at the infinity is studied by the Riemann-Hilbert approach. We consider the direct scattering problem, corresponding eigenfunctions, scattering matrix and establish some of their properties. These results are used in the construction of an associated Riemann-Hilbert problem. Assuming that the scattering coefficients possess single or double poles, we derive the problem solutions. Finally, we present graphical examples of 1-, 2- and 3-soliton solutions and discuss their propagation.

  • Keywords

Higher-order dispersive nonlinear Schrödinger equation, Riemann-Hilbert approach, soliton solutions.

  • AMS Subject Headings

35C08, 35Q15, 35Q51

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-369, author = {Li , Zhi-QiangTian , Shou-FuYang , Jin-Jie and Wang , Xiao-Li}, title = {Riemann-Hilbert Approach and Soliton Solutions of the Higher-Order Dispersive Nonlinear Schrödinger Equations with Single and Double Poles}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {2}, pages = {369--388}, abstract = {

The higher-order dispersive nonlinear Schrödinger equation with the zero boundary conditions at the infinity is studied by the Riemann-Hilbert approach. We consider the direct scattering problem, corresponding eigenfunctions, scattering matrix and establish some of their properties. These results are used in the construction of an associated Riemann-Hilbert problem. Assuming that the scattering coefficients possess single or double poles, we derive the problem solutions. Finally, we present graphical examples of 1-, 2- and 3-soliton solutions and discuss their propagation.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.240920.291120}, url = {http://global-sci.org/intro/article_detail/eajam/18639.html} }
TY - JOUR T1 - Riemann-Hilbert Approach and Soliton Solutions of the Higher-Order Dispersive Nonlinear Schrödinger Equations with Single and Double Poles AU - Li , Zhi-Qiang AU - Tian , Shou-Fu AU - Yang , Jin-Jie AU - Wang , Xiao-Li JO - East Asian Journal on Applied Mathematics VL - 2 SP - 369 EP - 388 PY - 2021 DA - 2021/02 SN - 11 DO - http://doi.org/10.4208/eajam.240920.291120 UR - https://global-sci.org/intro/article_detail/eajam/18639.html KW - Higher-order dispersive nonlinear Schrödinger equation, Riemann-Hilbert approach, soliton solutions. AB -

The higher-order dispersive nonlinear Schrödinger equation with the zero boundary conditions at the infinity is studied by the Riemann-Hilbert approach. We consider the direct scattering problem, corresponding eigenfunctions, scattering matrix and establish some of their properties. These results are used in the construction of an associated Riemann-Hilbert problem. Assuming that the scattering coefficients possess single or double poles, we derive the problem solutions. Finally, we present graphical examples of 1-, 2- and 3-soliton solutions and discuss their propagation.

Li , Zhi-QiangTian , Shou-FuYang , Jin-Jie and Wang , Xiao-Li. (2021). Riemann-Hilbert Approach and Soliton Solutions of the Higher-Order Dispersive Nonlinear Schrödinger Equations with Single and Double Poles. East Asian Journal on Applied Mathematics. 11 (2). 369-388. doi:10.4208/eajam.240920.291120
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