Inverse Scattering Method for Constructing Multisoliton Solutions of Higher-Order Nonlinear Schrödinger Equations
Year: 2023
Author: Xiu-Bin Wang, Shou-Fu Tian
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 213–229
Abstract
We develop an inverse scattering method for an integrable higher-order nonlinear Schrödinger equation (NLSE) with the zero boundary condition at the infinity. An appropriate Riemann-Hilbert problem is related to two cases of scattering data — viz. for $N$ simple poles and a one higher-order pole. This allows obtaining the exact formulae of $N$-th order position and soliton solutions in the form of determinants. In addition, special choices of free parameters allow determining remarkable characteristics of these solutions and discussing them graphically. The results can be also applied to other types of NLSEs such as the standard NLSE, Hirota equation, and complex modified KdV equation. They can help to further explore and enrich related nonlinear wave phenomena.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2021-351.270222
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 213–229
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Inverse scattering method Riemann-Hilbert problem soliton.