Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities

Pengfei Li*, Boris A. Malomed, Dumitru Mihalache

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We demonstrate that the fractional cubic-quintic nonlinear Schrödinger equation, characterized by its Lévy index, maintains ring-shaped soliton clusters (“necklaces") carrying orbital angular momentum. They can be built, in the respective optical setting, as circular chains of fundamental solitons linked by a vortical phase field. We predict semi-analytically that the metastable necklace-shaped clusters persist, corresponding to a local minimum of an effective potential of interaction between adjacent solitons in the cluster. Systematic simulations corroborate that the clusters stay robust over extremely large propagation distances, even in the presence of strong random perturbations.

Original languageEnglish
Pages (from-to)34472-34488
Number of pages17
JournalOptics Express
Issue number23
StatePublished - 9 Nov 2020


FundersFunder number
1331 Project" Key Innovative Research Team of Taiyuan Normal UniversityI0190364
Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi
Applied Basic Research Program of Sichuan Province201901D211424
National Natural Science Foundation of China11805141
Israel Science Foundation1286/17


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