Blowup and solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems
Journal
Physica D: Nonlinear Phenomena
Journal Volume
239
Journal Issue
10
Pages
613-626
Date Issued
2010
Author(s)
Abstract
Blowup ring profiles have been investigated by finding non-vortex blowup solutions of nonlinear Schrödinger equations (NLSEs) (cf. Fibich et al. (2005) [7] and Fibich et al. (2007) [8]). However, those solutions have infinite L2 norm, so one may not maintain the ring profile all the way up to the singularity. To find H1 non-vortex blowup solutions with ring profiles, we study the blowup solutions of two-component systems of NLSEs with nonlinear coefficients β and νj, j = 1, 2. When β < 0 and ν1 ≫ ν2 > 0, the two-component system can be transformed into a multi-scale system with fast and slow variables which may produce H1 blowup solutions with non-vortex ring profiles. We use the localized energy method with symmetry reduction to construct these solutions rigorously. On the other hand, these solutions may describe steady non-vortex bright ring solitons. Various types of ring profiles including m-ring and ring-ring profiles are presented by numerical solutions. © 2010 Elsevier B.V. All rights reserved.
SDGs
Type
journal article