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Title: Collapse for the higher-order nonlinear Schrödinger equation

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.
Authors:
 [1] ;  [2] ;  [1] ;  [3] ;  [2] ;  [4]
  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
Publication Date:
OSTI Identifier:
1234654
Report Number(s):
LA-UR--15-23187
Journal ID: ISSN 0167-2789; PII: S0167278915002328
Grant/Contract Number:
DMS-1312856; FP7; IRSES-605096; AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 0167-2789
Publisher:
Elsevier
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING