Abstract
In this paper, the effect of gain or loss on the dynamics of rogue waves is investigated by using the complex Ginzburg-Landau equation as a framework. Several external energy input mechanisms are studied, namely, constant background or compact Gaussian gains and a ‘rogue gain’ localized in space and time. For linear background gain, the rogue wave does not decay back to the mean level but evolves into peaks with growing amplitude. However, if such gain is concentrated locally, a pinned mode with constant amplitude could replace the time transient rogue wave and become a sustained feature. By restricting such spatially localized gain to be effective only for a finite time interval, a ‘rogue-wave-like’ mode can be recovered. On the other hand, if the dissipation is enhanced in the localized region, the formation of rogue wave can be suppressed. Finally, the effects of linear and cubic gain are compared. If the strength of the cubic gain is large enough, the rogue wave may grow indefinitely (‘blow up’), whereas the solution under a linear gain is always finite. In conclusion, the generation and dynamics of rogue waves critically depend on the precise forms of the external gain or loss.
Highlights
The propagation and dynamics of wave envelopes under the competing physical effects of dispersion, cubic nonlinearity, gain, and loss are applicable to many disciplines in physical science.The complex Ginzburg-Landau equation serves as a useful model and has been studied extensively [1].Many modes of a variety of properties have been established, ranging from localized pulses to fronts or kink type structures.Recently, rogue waves have been studied intensively as extreme and rare events in physics.Rogue waves will enhance our understanding of physical phenomena in many applied settings, ranging from maritime risk of large amplitude oceanic waves to modern technological advances in optics [2,3,4,5,6]
The most widely employed theoretical model is probably the nonlinear Schrödinger equation (NLSE), where the Peregrine breather represents a mode localized in both space and time
Most works focus on the case where the variable coefficients are functions of time (t) only [30], while some concentrate on the case of spatial dependence (x) alone [32]
Summary
The propagation and dynamics of wave envelopes under the competing physical effects of dispersion, cubic nonlinearity, gain, and loss are applicable to many disciplines in physical science. The most widely employed theoretical model is probably the nonlinear Schrödinger equation (NLSE), where the Peregrine breather represents a mode localized in both space and time. Besides the NLSE, several other nonlinear evolution systems, e.g., the Lugiato-Lefever equation (LLE) [10], have been employed as analytical models in studying dissipative rogue waves. ‘spiny solitons’ can chaotically generate spikes of large amplitude and short duration These spikes resemble rogue waves and have profiles, spectra, and autocorrelation functions different from other pulses studied earlier in the literature [18]. Such dissipative solitons with extreme spikes may occupy a significant portion of the parameter space of the cubic-quintic complex Ginzburg-Landau equation [17].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
