Collapse for the higherorder nonlinear Schrödinger equation
We examine conditions for finitetime collapse of the solutions of the higherorder nonlinear Schr odinger (NLS) equation incorporating thirdorder dispersion, selfsteepening, 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 zerostate, 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 longtime stability properties of localized solutions. The role of the higherorder effects to the transient dynamics is also revealed in these simulations.
 Authors:

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 Univ. of Athens (Greece). Dept. of Physics
 Univ. of the Aegean, Samos (Greece). Dept. of Mathematics
 Univ. of Ioannina (Greece). Dept. of Mathematics
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics
 Publication Date:
 Report Number(s):
 LAUR1523187
Journal ID: ISSN 01672789; PII: S0167278915002328
 Grant/Contract Number:
 DMS1312856; FP7; IRSES605096; AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physica. D, Nonlinear Phenomena
 Additional Journal Information:
 Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 01672789
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (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
 OSTI Identifier:
 1234654
 Alternate Identifier(s):
 OSTI ID: 1359739
Achilleos, V., Diamantidis, S., Frantzeskakis, D. J., Horikis, T. P., Karachalios, N. I., and Kevrekidis, P. G.. Collapse for the higherorder nonlinear Schrödinger equation. United States: N. p.,
Web. doi:10.1016/j.physd.2015.11.005.
Achilleos, V., Diamantidis, S., Frantzeskakis, D. J., Horikis, T. P., Karachalios, N. I., & Kevrekidis, P. G.. Collapse for the higherorder nonlinear Schrödinger equation. United States. doi:10.1016/j.physd.2015.11.005.
Achilleos, V., Diamantidis, S., Frantzeskakis, D. J., Horikis, T. P., Karachalios, N. I., and Kevrekidis, P. G.. 2016.
"Collapse for the higherorder nonlinear Schrödinger equation". United States.
doi:10.1016/j.physd.2015.11.005. https://www.osti.gov/servlets/purl/1234654.
@article{osti_1234654,
title = {Collapse for the higherorder nonlinear Schrödinger equation},
author = {Achilleos, V. and Diamantidis, S. and Frantzeskakis, D. J. and Horikis, T. P. and Karachalios, N. I. and Kevrekidis, P. G.},
abstractNote = {We examine conditions for finitetime collapse of the solutions of the higherorder nonlinear Schr odinger (NLS) equation incorporating thirdorder dispersion, selfsteepening, 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 zerostate, 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 longtime stability properties of localized solutions. The role of the higherorder effects to the transient dynamics is also revealed in these simulations.},
doi = {10.1016/j.physd.2015.11.005},
journal = {Physica. D, Nonlinear Phenomena},
number = C,
volume = 316,
place = {United States},
year = {2016},
month = {2}
}