Stabilization mechanism for two-dimensional solitons in nonlinear parametric resonance

Details Stabilization mechanism for two-dimensional solitons in nonlinear parametric resonance Stabilization mechanism for two-dimensional solitons in nonlinear parametric resonance

2004-10-21

arxiv.org/abs/nlin/0410044v1

Nonlinear Sciences

Pattern Formation and Solitons

10 pages, 2 figures

Scientific paper

10.1007/s11232-005-0137-3

We consider a simple model system supporting stable solitons in two dimensions. The system is the parametrically driven damped nonlinear Schr\"odinger equation, and the soliton stabilises for sufficiently strong damping. The purpose of this note is to elucidate the stabilisation mechanism; we do this by reducing the partial differential equation to a finite-dimensional dynamical system. Our conclusion is that the negative feedback loop occurs via the enslaving of the soliton's phase, locked to the driver, to its amplitude and width.

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