Inverse scattering transform of an extended nonlinear Schrodinger equation with nonzero boundary conditions and its multisoliton solutions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Wang, Xiu-Bin¹  Han, Bo¹ 

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

关键词: Inverse scattering transform;    Soliton solutions;    Riemann-Hilbert problem;   

DOI  :  10.1016/j.jmaa.2020.123968

来源: Elsevier

【 摘 要 】

Under investigation in this work is an extended nonlinear Schrodinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation with nonzero boundary conditions at infinity is systematically discussed. Then the inverse problems are solved through the investigation of the matrix Riemann-Hilbert problem. Therefore, the general solutions for the potentials, and explicit expressions for the reflection-less potentials are presented. Furthermore, we construct the simple-pole and double-pole solutions for the equation. Finally, the remarkable characteristics of these solutions are graphically discussed. Our results should be useful to enrich and explain the related nonlinear wave phenomena in nonlinear fields. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free