Soliton dynamics in a fractional complex Ginzburg-Landau model

Yunli Qiu, Boris A. Malomed, Dumitru Mihalache, Xing Zhu, Li Zhang, Yingji He*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The general objective of the work is to study dynamics of dissipative solitons in the framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional order. To estimate the shape of solitons in fractional models, we first develop the variational approximation for solitons of the fractional nonlinear Schrödinger equation (NLSE), and an analytical approximation for exponentially decaying tails of the solitons. Proceeding to numerical consideration of solitons in fractional CGLE, we study, in necessary detail, effects of the respective Lévy index (LI) on the solitons’ dynamics. In particular, dependence of stability domains in the model's parameter space on the LI is identified. Pairs of in-phase dissipative solitons merge into single pulses, with the respective merger distance also determined by LI.

Original languageEnglish
Article number109471
JournalChaos, Solitons and Fractals
StatePublished - Feb 2020


  • Dissipative solitons
  • Effective diffusion
  • Fractional complex Ginzburg-Landau equation


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