Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 58: Poster: Nonlinear Dynamics; Pattern Formation; Networks; Delay Systems; Synchronization

DY 58.7: Poster

Thursday, March 19, 2020, 15:00–18:00, P1C

Hidden Markov dynamics of the chaotic diffusion of dissipative solitons — •Tony Albers¹, Jaime Cisternas², and Günter Radons¹ — ¹Institute of Physics, Chemnitz University of Technology, Chemnitz, Germany — ²Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile

Dissipative solitons are persistent localized solutions which are the result of a complicated balance between dispersion and nonlinear effects as well as dissipation and energy gain. These structures can show interesting dynamical behaviors such as explosions, i.e., transient enlargements of the solitons that lead to spatial displacements if the explosions are asymmetric. Due to the chaotic nature of the underlying soliton dynamics, the sequence of spatial jumps as well as the interexplosion times seem to be random thus leading to a random-walk kind of motion [1]. In this contribution, we show that the sequence of spatial shifts of exploding dissipative solitons in a prototypical complex Ginzburg-Landau equation, known, e.g., from nonlinear optics, is governed by a hidden Markov process with continuous output densities. It captures the non-trivial decay of correlations of jump widths and symbol sequences representing the soliton motion, the statistics of anti-persistent walk episodes and the multimodal density of the jump widths. This is the first example of a physically meaningful reduction of an infinite-dimensional deterministic dynamics to one of a probabilistic finite state machine.

[1] Tony Albers, Jaime Cisternas and Günter Radons, New J. Phys. 21 103034 (2019)