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AuthorAnastassi, Z.A.
AuthorFotopoulos, G.
AuthorFrantzeskakis, D.J.
AuthorHorikis, T.P.
AuthorKarachalios, N.I.
AuthorKevrekidis, P.G.
AuthorStratis, I.G.
AuthorVetas, K.
Available date2020-11-19T08:53:09Z
Publication Date2017
Publication NamePhysica D: Nonlinear Phenomena
ResourceScopus
ISSN1672789
URIhttp://dx.doi.org/10.1016/j.physd.2017.06.003
URIhttp://hdl.handle.net/10576/17000
AbstractWe consider the asymptotic behavior of the solutions of a nonlinear Schrödinger (NLS) model incorporating linear and nonlinear gain/loss. First, we describe analytically the dynamical regimes (depending on the gain/loss strengths), for finite-time collapse, decay, and global existence of solutions. Then, for all the above parametric regimes, we use direct numerical simulations to study the dynamics corresponding to algebraically decaying initial data. We identify crucial differences between the dynamics of vanishing initial conditions, and those converging to a finite constant background: in the former (latter) case we find strong (weak) collapse or decay, when the gain/loss parameters are selected from the relevant regimes. One of our main results, is that in all the above regimes, non-vanishing initial data transition through spatiotemporal, algebraically decaying waveforms. While the system is nonintegrable, the evolution of these waveforms is reminiscent to the evolution of the Peregrine rogue wave of the integrable NLS limit. The parametric range of gain and loss for which this phenomenology persists is also touched upon.
SponsorWe would like to thank the referees for valuable comments. The authors Z.A.A., G.F., D.J.F., N.I.K., P.G.K., I.G.S. and K.V., acknowledge that this work wasmade possible by NPRP grant # [ 8-764-160 ] from Qatar National Research Fund (a member of Qatar Foundation). The findings achieved herein are solely the responsibility of the authors. D.J.F. and P.G.K. gratefully acknowledge the support of the "Greek Diaspora Fellowship Program" of Stavros Niarchos Foundation. Appendix A
Languageen
PublisherElsevier B.V.
SubjectGain/loss
NLS equation
Nonlinear optics
Rogue waves
TitleSpatiotemporal algebraically localized waveforms for a nonlinear Schrödinger model with gain and loss
TypeArticle
Pagination24-33
Volume Number355
dc.accessType Abstract Only


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