2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80851The parametrically driven damped nonlinear Schrödinger 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.10 pages, 6 figures, submitted to Lecture Notes in Computer SciencePattern Formation and Solitonstext