2018/12/12 by G. Fotopoulos, Georgios Fotopoulos, Fotopoulos, G. +11
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS
paper · pdf · doi:10.48550/arxiv.1812.05439
arXiv admin note: text overlap with arXiv:1811.09812
openalex publication_date 2018/12/12 · arxiv created 2019/10/16 · arxiv updated 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We perform a numerical study of the initial-boundary value problem, with vanishing boundary conditions, of a driven nonlinear Schrödinger equation (NLS) with linear damping and a Gaussian driver. We identify Peregrine-like rogue waveforms, excited by two different types of vanishing initial data decaying at an algebraic or exponential rate. The observed extreme events emerge on top of a decaying support. Depending on the spatial/temporal scales of the driver, the transient dynamics -- prior to the eventual decay of the solutions -- may resemble the one in the semiclassical limit of the integrable NLS, or may, e.g., lead to large-amplitude breather-like patterns. The effects of the damping strength and driving amplitude, in suppressing or enhancing respectively the relevant features, as well as of the phase of the driver in the construction of a diverse array of spatiotemporal patterns, are numerically analyzed.