Nodal two-dimensional solitons in nonlinear parametric resonance
Pattern Formation and Solitons
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.nlin/0410012,
title = {Nodal two-dimensional solitons in nonlinear parametric resonance},
author = {N. V. Alexeeva and E. V. Zemlyanaya},
journal= {arXiv preprint arXiv:nlin/0410012},
year = {2007}
}
Comments
10 pages, 6 figures, submitted to Lecture Notes in Computer Science