WIAS Preprint No. 2843, (2021)

Dissipative soliton interaction in Kerr resonators with high-order dispersion


  • Vladimirov, Andrei G.
    ORCID: 0000-0002-7540-8380
  • Tlidi, Mustapha
    ORCID: 0000-0003-3660-2524
  • Taki, Majid
    ORCID: 0000-0002-2522-1999

2020 Mathematics Subject Classification

  • 78A60 35Q55 35Q60

2010 Physics and Astronomy Classification Scheme

  • 42.60.Fc


  • Haus master equation, mode-locking, class B laser, multiscale method




We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato--Lefever equation with fourth order dispersion We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourth-order dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the bound state stability.

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