Nodal two-dimensional solitons in nonlinear parametric resonance

Details Nodal two-dimensional solitons in nonlinear parametric resonance Nodal two-dimensional solitons in nonlinear parametric resonance

2004-10-11

arxiv.org/abs/nlin/0410012v1

Nonlinear Sciences

Pattern Formation and Solitons

10 pages, 6 figures, submitted to Lecture Notes in Computer Science

Scientific paper

The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that although the nodal solitons are stable against radially-symmetric perturbations for sufficiently large damping coefficients, they are always unstable to azimuthal perturbations. The corresponding break-up scenarios are studied using direct numerical simulations. Typically, the nodal solutions break into symmetric "necklaces" of stable nodeless solitons.

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