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 -

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.