Collapse for the higher-order nonlinear Schrödinger equation

Journal Article · Mon Feb 01 00:00:00 EST 2016 · Physica. D, Nonlinear Phenomena

DOI:https://doi.org/10.1016/j.physd.2015.11.005· OSTI ID:1234654

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

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1. Univ. of Athens (Greece). Dept. of Physics
2. Univ. of the Aegean, Samos (Greece). Dept. of Mathematics
3. Univ. of Ioannina (Greece). Dept. of Mathematics
4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr odinger (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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: DMS-1312856; FP7; IRSES-605096; AC52-06NA25396
• OSTI ID: 1234654
• Alternate ID(s): OSTI ID: 1359739
• Report Number(s): LA-UR-15-23187; PII: S0167278915002328
• Journal Information: Physica. D, Nonlinear Phenomena, Vol. 316, Issue C; ISSN 0167-2789
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

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