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

TL;DR

This paper analytically investigates rogue waves and rational solitons in an integrable fifth-order nonlinear Schrödinger equation, revealing new solutions and their dynamics, with implications for nonlinear fiber optics.

Contribution

It introduces novel first- and second-order rogue wave solutions for the FONLS equation, including trajectories and profiles, extending understanding of integrable nonlinear wave models.

Findings

New rogue wave solutions with detailed trajectories

Conditions for modulation instability in the FONLS model

Predictions of dynamical phenomena in nonlinear fiber optics

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.