Abstract
The 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.
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Alexeeva, N.V., Zemlyanaya, E.V. (2005). Nodal Two-Dimensional Solitons in Nonlinear Parametric Resonance. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_9
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DOI: https://doi.org/10.1007/978-3-540-31852-1_9
Publisher Name: Springer, Berlin, Heidelberg
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