Nodal two-dimensional solitons in nonlinear parametric resonance

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dc.creatorAlexeeva, N. V.
dc.creatorZemlyanaya, E. V.
dc.date2004-10-11
dc.date.accessioned2026-07-07T05:36:01Z
dc.date.available2026-07-07T05:36:01Z
dc.descriptionThe 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.
dc.description10 pages, 6 figures, submitted to Lecture Notes in Computer Science
dc.identifierhttps://arxiv.org/abs/nlin/0410012
dc.identifierhttp://arxiv.org/abs/nlin/0410012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80851
dc.subjectPattern Formation and Solitons
dc.titleNodal two-dimensional solitons in nonlinear parametric resonance
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