Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation
Abstract
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Keywords
Cite
@article{arxiv.1509.05886,
title = {Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation},
author = {Yunqing Yang and Zhenya Yan and Boris A. Malomed},
journal= {arXiv preprint arXiv:1509.05886},
year = {2017}
}
Comments
11 pages, 14 figures: Chaos (to be published in Oct. 2015)