We investigate the dynamics of dissipative solitons in the cubicquintic complex Ginzburg-Landau equation in one spatial dimension for different values of the bifurcation parameter μ. We consider a certain range of the parameter μ where dissipative solitons show explosions, i.e. transient enlargements of the soliton that lead to spatial shifts if the explosions are asymmetric. We find that depending on the parameter μ, the arising sequence of spatial shifts can be modeled by a simple anti-persistent random walk or by a more complicated hidden Markov model. We show with the help of exact analytical calculations that these models are able to reproduce several statistics of the soliton motion such as the distribution of spatial shifts, the correlation of spatial shifts, and the distribution of zig-zag streaks.
|Journal of Statistical Mechanics: Theory and Experiment
|Published - 10 Sep 2019
- correlation functions
- dissipative systems
- nonlinear dynamics