Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Li Wang,Beijing Institute of Mathematical Sciences and Applications
Inviter:
Title:	Parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media
Language:	Chinese
Time & Venue:	2023.05.30 11:00-12:00 N402
Abstract:	We consider a NLS equation with critical or supercritical nonlinearity. A family of solitons, which are unstable in this setting against the critical or supercritical collapse, is stabilized by pinning to an attractive defect, that may also include a PT-symmetric gain-loss component. For the attractive defect with the delta-functional profile, a full family of the pinned solitons is found in an exact analytical form. In the absence of the gain-loss term, the solitons’ stability is investigated in an analytical form too, by means of the VK criterion; in the presence of the PT -balanced gain and loss, the stability is explored by means of numerical methods. In particular, the entire family of pinned solitons is stable in the quintic (critical) medium if the gain-loss term is absent. A stability region for the pinned solitons persists in the model with an arbitrarily high power of the self-focusing nonlinearity.