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 Schrödinger (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.

11 pages, 14 figures: Chaos (to be published in Oct. 2015)

References in corpus (4)

• Rogue waves emerging from the resonant interaction of three waves
• Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation
• Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrodinger equation with modulating coefficients
• Trajectory Characters of Rogue Waves

Cited by in corpus (16)

• Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
• Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: exact solutions and stability
• Higher-order rational solitons and rogue-like wave solutions of the (2+1)-dimensional nonlinear fluid mechanics equations
• General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system
• Stable Soliton Excitations in Modulational Instability Regime with the Fourth-order Effects
• Higher-order vector Peregrine solitons and asymptotic estimates for the multi-component nonlinear Schrödinger equations
• Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves
• Growth rate of modulation instability driven by superregular breathers
• Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrodinger equation
• Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations
• Modulation instability and solitons in two-color nematic crystals
• GHW-based Necessary and Sufficient Conditions for Support Constrained Generator Matrices
• Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing
• Exciting extreme events in the damped and AC-driven NLS equation through plane wave initial conditions
• Rogue waves in extended Gross-Pitaevskii Models with a Lee-Huang-Yang correction
• The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions