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

Abstract

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.

arXiv comment19 pages, 8 figures

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Cited by in corpus (2)

• Double and triple poles solutions for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions
• The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions