Spontaneous motion of localized structures induced by parity symmetry transition

TL;DR

This paper investigates how parity symmetry breaking induces spontaneous motion in localized structures within a nonvariational Swift-Hohenberg model, revealing a supercritical transition from stationary to moving states.

Contribution

It demonstrates the supercritical nature of the transition and provides analytical and numerical characterization of the bifurcation leading to asymmetric moving localized structures.

Findings

Transition from stationary to moving localized structures due to parity breaking

Supercritical bifurcation scenario identified and characterized

Extension discussion for two-dimensional systems

Abstract

We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized structures in one spatial dimension as a result of a parity breaking instability. This behavior is attributed to the nonvariational character of the model. We show that the nature of this transition is supercritical. We characterize analytically and numerically this bifurcation scenario from which emerges asymmetric moving localized structures. A generalization for two-dimensional settings is discussed.