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

TL;DR

This paper investigates how third-order dispersion in a fiber-laser cavity model creates stable and oscillatory bound states of dissipative solitons, revealing multistability, bifurcations, and chaotic dynamics.

Contribution

It demonstrates the existence of multiple families of bound soliton states induced solely by third-order dispersion in a complex Ginzburg-Landau model.

Findings

Stable bound states only exist with third-order dispersion.

Bound states transition to oscillatory and chaotic states via bifurcations.

Multistable three- and four-soliton complexes are identified.

Abstract

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, including the third-order 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 four-soliton 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.