A hidden Markov model for the dynamics of diffusing dissipative solitons

Tony Albers, Jaime Cisternas, Günter Radons

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.
Original languageAmerican English
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2019
Issue number9
DOIs
StatePublished - 10 Sep 2019

Keywords

  • correlation functions
  • diffusion
  • dissipative systems
  • nonlinear dynamics

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