Riemann-Hilbert Approach and Soliton Solutions of the Higher-Order Dispersive Nonlinear Schrödinger Equations with Single and Double Poles
Year: 2021
Author: Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang, Xiao-Li Wang
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.240920.291120
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 369–388
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Higher-order dispersive nonlinear Schrödinger equation Riemann-Hilbert approach soliton solutions.
Author Details
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https://doi.org/10.1007/s11071-022-07363-0 [Citations: 8]