Spatiotemporal algebraically localized waveforms for a nonlinear Schrodinger model with gain and loss

PHYSICA D-NONLINEAR PHENOMENA

卷:355

Article

Anastassi, Z. A.¹  Fotopoulos, G.¹  Frantzeskakis, D. J.²  Horikis, T. P.³  Karachalios, N. I.⁴  Kevrekidis, P. G.⁵  Stratis, I. G.⁶  Vetas, K.^1,4 

[1] Qatar Univ, Dept Math Stat & Phys, Coll Arts & Sci, POB 2713, Doha, Qatar

[2] Natl & Kapodistrian Univ Athens, Dept Phys, Athens 15784, Greece

[3] Univ Ioannina, Dept Math, GR-45110 Ioannina, Greece

[4] Univ Aegean, Dept Math, Karlovassi 83200, Samos, Greece

[5] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[6] Natl & Kapodistrian Univ Athens, Dept Math, Athens 15784, Greece

关键词: NLS equation;    Gain/loss;    Rogue waves;    Nonlinear optics;   

DOI  :  10.1016/j.physd.2017.06.003

来源: Elsevier

【 摘 要 】

We consider the asymptotic behavior of the solutions of a nonlinear Schrodinger (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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free