Stabilization Mechanism for Two-Dimensional Solitons in Nonlinear Parametric Resonance |
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Authors: | N V Alexeeva |
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Institution: | (1) Department of Mathematics, University of Cape Town, South Africa |
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Abstract: | We consider a simple model system supporting stable solitons in two dimensions. The system is the parametrically driven damped
nonlinear Schrodinger equation, and the soliton stabilizes for sufficiently strong damping. We elucidate the stabilization
mechanism by reducing the partial differential equation to a finite-dimensional dynamical system and conclude that the negative
feedback loop occurs via enslaving the soliton phase, locked to the driver, to its amplitude and width.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 226–233, August, 2005. |
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Keywords: | Faraday resonance driven damped nonlinear Schrodinger equation oscillons stability |
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