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arXiv · 1509.05886

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

Yunqing Yang·Zhenya Yan·Boris A. Malomed
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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.

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Yunqing Yang, Zhenya Yan, Boris A. Malomed. 2015-09-19. Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation. https://doi.org/10.1063/1.4931594

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