Collapse for the higher-order nonlinear Schrodinger equation

PHYSICA D-NONLINEAR PHENOMENA

卷:316

Article

Achilleos, V.¹  Diamantidis, S.²  Frantzeskakis, D. J.¹  Horikis, T. P.³  Karachalios, N. I.²  Kevrekidis, P. G.^4,5,6 

[1] Univ Athens, Dept Phys, Athens 15784, Greece

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

[3] Univ Ioannina, Dept Math, POB 1186, GR-45110 Ioannina, Greece

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

[5] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA

[6] Ctr Non Linear Studies, Los Alamos, NM 87545 USA

关键词: Collapse;    Instabilities;    Solitons;    Nonlinear optics;   

DOI  :  10.1016/j.physd.2015.11.005

来源: Elsevier

【 摘 要 】

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schrodinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher order effects to the transient dynamics is also revealed in these simulations. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free