Dynamics of Localized Structures in Systems with Broken Parity Symmetry

TL;DR

This paper explores how the dynamics and interactions of localized structures in nonlinear dissipative systems are fundamentally altered when parity symmetry is broken, revealing new behaviors and control mechanisms.

Contribution

It extends the analysis of localized structures to systems without parity symmetry, showing new velocity behaviors and interaction asymmetries.

Findings

LS drifting speed depends on parameter value, not just gradient

Broken symmetry introduces new velocity contributions

LS interactions become asymmetrical and repulsive

Abstract

A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these Localized Structures (LSs) have been investigated so far in situations featuring parity symmetry. In this letter we extend this analysis to systems lacking of this property. We show that the LS drifting speed in a parameter varying landscape is not simply proportional to the parameter gradient, as found in parity preserving situations. The symmetry breaking implies a new contribution to the velocity field which is a function of the parameter value, thus leading to a new paradigm for LSs manipulation. We illustrate this general concept by studying the trajectories of the LSs found in a passively mode-locked laser operated in the localization regime. Moreover, the lack of parity affects significantly LSs interactions which are governed by asymmetrical repulsive forces.