Stationary and oscillatory bound states of dissipative solitons created by thirdorder dispersion
Abstract
We consider the model of fiberlaser cavities near the zerodispersion point, based on the complex GinzburgLandau equation with the cubicquintic nonlinearity, including the thirdorder dispersion (TOD) term. It is well known that this model supports stable dissipative solitons. We demonstrate that the same model gives rise to several families of robust bound states of the solitons, which exists only in the presence of the TOD. There are both stationary and dynamical bound states, with oscillating separation between the bound solitons. Stationary states are multistable, corresponding to different values of the separation. With the increase of the TOD coefficient, the bound state with the smallest separation gives rise the oscillatory state through the Hopf bifurcation. Further growth of TOD leads to a bifurcation transforming the oscillatory limit cycle into a strange attractor, which represents a chaotically oscillating dynamical bound state. Families of multistable three and foursoliton complexes are found too, the ones with the smallest separation between the solitons again ending by a transition to oscillatory states through the Hopf bifurcation.
 Publication:

Optics Letters
 Pub Date:
 June 2018
 DOI:
 10.1364/OL.43.002688
 arXiv:
 arXiv:1805.02190
 Bibcode:
 2018OptL...43.2688S
 Keywords:

 Physics  Optics;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 to be published in Optics Letters