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Optica Publishing Group
  • CLEO/Europe and EQEC 2009 Conference Digest
  • (Optica Publishing Group, 2009),
  • paper EF4_2

Modulational Instability of Bright Solitons of the Hyperbolic Nonlinear Schrödinger Equation

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Symmetry-breaking instability is one of the most remarkable physical phenomena that may occur in nonlinear media. Among these phenomena, the symmetry-breaking instability of plane solitary waves has attracted particular attention and was first formulated for soliton solutions of the nonlinear Schrödinger (NLS) equation by Zakharov and Rubenchik [1]. More specifically they predicted that in normally dispersive nonlinear media, i. e. in systems ruled by the hyperbolic nonlinear Schrödinger equation, the nonlinear space-time coupling leads to the growth of lateral oscillations of the soliton beam, known as snake instability. Recently, the full instability gain spectrum of solitons of the (2+l)-dimensional hyperbolic NLS equation has been theoretically predicted and it was shown that solitons are unstable against perturbations of arbitrary high frequencies [2]. Moreover, it has been shown that a threshold separates the snake instability regime that occurs in the long wavelength range of perturbations from the “oscillating” snake instability regime.

© 2009 IEEE

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