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

Under investigation in this work is an extended nonlinear Schrödinger 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 dis...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-07, Vol.487 (1), p.123968, Article 123968
Main Authors: Wang, Xiu-Bin, Han, Bo
Format: Article
Language:English
Subjects:
Inverse scattering transform
Riemann-Hilbert problem
Soliton solutions
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Summary:Under investigation in this work is an extended nonlinear Schrödinger 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.123968