Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation

Yunqing Yang, Zhenya Yan*, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel 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.

Original languageEnglish
Article number103112
JournalChaos
Volume25
Issue number10
DOIs
StatePublished - Oct 2015

Funding

FundersFunder number
National Natural Science Foundation of China11326165, 11202178, 61178091

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