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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 15, Iss. 11 — Nov. 1, 1998
  • pp: 2757–2762

Instability mechanism for bright solitary-wave solutions to the cubic–quintic Ginzburg–Landau equation

Todd Kapitula and Björn Sandstede  »View Author Affiliations


JOSA B, Vol. 15, Issue 11, pp. 2757-2762 (1998)
http://dx.doi.org/10.1364/JOSAB.15.002757


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Abstract

We address the stability of solitary waves to the complex cubic–quintic Ginzburg–Landau equation near the nonlinear Schrödinger limit. It is shown that the adiabatic method does not capture all possible instability mechanisms. The solitary wave can destabilize owing to discrete eigenvalues that move out of the continuous spectrum upon adding nonintegrable perturbations to the nonlinear Schrödinger equation. If an eigenvalue does move out of the continuous spectrum, then we say that an edge bifurcation has occurred. We present a novel analytical technique that allows us to determine whether eigenvalues arise in such a fashion, and if they do, to locate them. Using this approach, we show that Hopf bifurcations can arise in the cubic–quintic Ginzburg–Landau equation.

© 1998 Optical Society of America

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Citation
Todd Kapitula and Björn Sandstede, "Instability mechanism for bright solitary-wave solutions to the cubic–quintic Ginzburg–Landau equation," J. Opt. Soc. Am. B 15, 2757-2762 (1998)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-15-11-2757


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