Collapse for the higher-order nonlinear Schrödinger equation

Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G.

doi:10.1016/j.physd.2015.11.005

Title: Collapse for the higher-order nonlinear Schrödinger equation

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Abstract

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:

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

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:: Mon Feb 01 00:00:00 EST 2016

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1234654

Alternate Identifier(s):: OSTI ID: 1359739

Report Number(s):: LA-UR-15-23187
Journal ID: ISSN 0167-2789; PII: S0167278915002328

Grant/Contract Number:: DMS-1312856; FP7; IRSES-605096; AC52-06NA25396

Resource 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

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Achilleos, V., Diamantidis, S., Frantzeskakis, D. J., Horikis, T. P., Karachalios, N. I., and Kevrekidis, P. G. Collapse for the higher-order nonlinear Schrödinger equation.  United States: N. p., 2016. 
Web.  doi:10.1016/j.physd.2015.11.005.

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                    Achilleos, V., Diamantidis, S., Frantzeskakis, D. J., Horikis, T. P., Karachalios, N. I., & Kevrekidis, P. G. Collapse for the higher-order nonlinear Schrödinger equation.  United States.  https://doi.org/10.1016/j.physd.2015.11.005

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                    Achilleos, V., Diamantidis, S., Frantzeskakis, D. J., Horikis, T. P., Karachalios, N. I., and Kevrekidis, P. G. Mon .  
"Collapse for the higher-order nonlinear Schrödinger equation".  United States.  https://doi.org/10.1016/j.physd.2015.11.005.  https://www.osti.gov/servlets/purl/1234654.

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@article{osti_1234654,

  title        = {Collapse for the higher-order 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 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.},

  doi          = {10.1016/j.physd.2015.11.005},

  journal      = {Physica. D, Nonlinear Phenomena},

  number       = C,

  volume       = 316,

  place        = {United States},

  year         = {Mon Feb 01 00:00:00 EST 2016},

  month        = {Mon Feb 01 00:00:00 EST 2016}

}

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