Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2001-12-28
Nonlinear Sciences
Pattern Formation and Solitons
4 pages; 1 figure
Scientific paper
10.1103/PhysRevLett.89.104101
We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.
Alexeeva Natalia V.
Barashenkov Igor V.
Zemlyanaya E. V.
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