TY - JOUR
T1 - Inverse Scattering Method for Constructing Multisoliton Solutions of Higher-Order Nonlinear Schrödinger Equations
AU - Wang , Xiu-Bin
AU - Tian , Shou-Fu
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 213
EP - 229
PY - 2023
DA - 2023/04
SN - 13
DO - http://doi.org/10.4208/eajam.2021-351.270222 
UR - https://global-sci.org/intro/article_detail/eajam/21645.html
KW - Inverse scattering method, Riemann-Hilbert problem, soliton.
AB - <p style="text-align: justify;">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.</p>