Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management

Abstract

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) selfdefocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.

Physics Letters A, on press

References in corpus (9)

• Dispersive shock waves and modulation theory
• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• Observation of a gradient catastrophe generating solitons
• Universal Peregrine soliton structure in nonlinear pulse compression in optical fiber
• Multidimensional solitons: Well-established results and novel findings
• Nonlinearity Management in Optics: Experiment, Theory, and Simulation
• The theory of optical dispersive shock waves in photorefractive media
• Modulational instability in a layered Kerr medium: Theory and Experiment
• Floquet Analysis of Kuznetsov--Ma breathers: A Path Towards Spectral Stability of Rogue Waves

Cited by in corpus (5)

• Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions
• Spatially modulated two- and three-component Rabi-coupled Gross-Pitaevskii systems
• Dispersion Managed Generation of Peregrine Solitons and Kuznetsov-Ma Breather in an Optical Fiber
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing