Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion

Hidetsugu Sakaguchi, Dmitry V. Skryabin, Boris A. Malomed*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the model of fiber-laser cavities near the zero-dispersion point, based on the complex Ginzburg–Landau equation with the cubic-quintic nonlinearity and third-order dispersion (TOD) term. It is known that this model supports stable dissipative solitons. We demonstrate that the same model gives rise to several specific families of robust bound states of solitons. There are both stationary and dynamical bound states, with constant or oscillating separation between the bound solitons. Stationary states are multistable, corresponding to different values of the separation. Following the increase of the TOD coefficient, the stationary bound state with the smallest separation gives rise to the oscillatory one through the Hopf bifurcation. Further growth of TOD leads to a bifurcation transforming the oscillatory bound state into a chaotically oscillating one. Families of multistable three- and four-soliton complexes are found too, the ones with the smallest separation between the solitons again ending by the transition to oscillatory states through the Hopf bifurcation.

Original languageEnglish
Pages (from-to)2688-2691
Number of pages4
JournalOptics Letters
Issue number11
StatePublished - 1 Jun 2018


FundersFunder number
EU H2020691011-Soliring
Horizon 2020 Framework Programme691011
Japan Society for the Promotion of Science18K03462
Russian Foundation for Basic Research17-02-00081
Israel Science Foundation1286/17
Government Council on Grants, Russian Federation074-U01
Erzincan Üniversitesi
Amt der Steiermärkischen Landesregierung


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