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Solitons in curved space of constant curvature

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Batz,  Sascha
Nonlinear Optics and Nanophotonics, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Peschel,  Ulf
Nonlinear Optics and Nanophotonics, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Batz, S., & Peschel, U. (2010). Solitons in curved space of constant curvature. PHYSICAL REVIEW A, 81(5): 053806. doi:10.1103/PhysRevA.81.053806.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002D-6B0B-8
Abstract
We consider spatial solitons as, for example, self-confined optical beams in spaces of constant curvature, which are a natural generalization of flat space. Due to the symmetries of these spaces we are able to define respective dynamical parameters, for example, velocity and position. For positively curved space we find stable multiple-hump solitons as a continuation from the linear modes. In the case of negatively curved space we show that no localized solution exists and a bright soliton will always decay through a nonlinear tunneling process.