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

Anastassi, Zacharias
Fotopoulos, G.
Frantzeskakis, D. J.
Horikis, T. P.
Karachalios, N. I.
Kevrekidis, P. G.
Stratis, I. G.
Vetas, K.
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Peer reviewed
We 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.
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.
NLS equation, Gain/loss, Rogue waves, Nonlinear optics, Computer simulation
Anastassi, Z.A., Fotopoulos, G., Frantzeskakis, D.J., Horikis, T.P., Karachalios, N.I., Kevrekidis, P.G., Stratis, I.G. and Vetas, K. (2017) Spatiotemporal algebraically localized waveforms for a nonlinear Schrödinger model with gain and loss. Physica D, 355, pp. 24-33.
Research Institute
Institute of Artificial Intelligence (IAI)